graphed to have two shells cross paths at a height of 160 feet and explode at an apex of 200 feet under normal weather conditions. If the shells have a launch angle θ = 60° above the horizontal, determine the common launch spee
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A fireworks show is choreographed to have two shells cross paths at a height of 160 feet and explode at an apex of 200 feet under normal weather conditions. If the shells have a launch angle θ = 60° above the horizontal, determine the common launch speed v0 for the shells, the separation distance d between the launch points A and B, and the time t from launch at which the shells explode.
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- A fireworks show is choreographed to have two shells cross paths at a height of 104 feet and explode at an apex of 151 feet under normal weather conditions. If the shells have a launch angle θ = 54° above the horizontal, determine the common launch speed v0 for the shells, the separation distance d between the launch points A and B, and the time t from launch at which the shells explode. Determine the common launch speed v0 for the shells.Batman’s missile is launched at a velocity of 20 m/s in a direction making an angle of 25° upward with the horizontal.a) What is the horizontal range (maximum x above ground) of the missile?b) What is the magnitude of the velocity of the missile just before it hits the ground?SITUATION 10. A fireworks show is choreographed to have two shells cross paths at a height of 160 feet and explode at an apex of 200 feet under normal weather conditions. If the shells have a launch angle theta = 60° above the horizontal, determine the common launch speed vo for the shells, the separation distance d between the launch points A and B, and the time from launch at which the shells explode. T 40' # 160' U0 e B
- A projectile is shot from ground level at 100 ft/s at a launch angle of θ that is between θ and π /2. Assume that the projectile is acted on by gravity, but not air resistance. Then, in a simple projectile-motion model it can be shown that the projectile lands at a distance R(θ) = 625 sinθcosθ ft from the launch point. What is the rate of change of the range with respect to the launch angle? For what angles does the range increase/decrease with increasing launch angle? What angle provides the maximum range, and what is that maximum range?A projectile is launched from a height H above the ground with speed V0 at an angle ao above the horizontal. In this problem, use a coordinate system where +y direction is upward. the+x direction is along the horizontal and to the right, and the x-coordinate of the projectile is initially zero. In this example, the maximum height reached by the projectile and the range of a projectile was calculated for a projectile launched from a height H above the ground and at an angle ao above the horizontal line. Calculate the time of flight, range, R, and maximum height, yMAX, reached by the projectile for the following special cases: a) Case 1: The projectile launched from the ground (H=0) b) Case 2: The projectile is launched horizontally (ao = 0)A skateboarder shoots off a ramp with a velocity of 5.5 m/s, directed at an angle of 63° above the horizontal. The end of the ramp is 1.1 m above the ground. Let the x-axis be parallel to the ground, the +y direction be vertically upward, and take as the origin the point on the ground directly below the top of the ramp. (a) How high above the ground is the highest point that the skateboarder reaches? (b) When the skateboarder reaches the highest point, how far is this point horizontally from the end of the ramp?
- You can use any coordinate system you like in order to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity v at an angle ? with respect to the horizontal. Let the building be 54.0 m tall, the initial horizontal velocity be 8.60 m/s, and the initial vertical velocity be 12.5 m/s. Choose your coordinates such that the positive y-axis is upward, and the x-axis is to the right, and the origin is at the point where the ball is released. (a) With these choices, find the ball's maximum height above the ground and the time it takes to reach the maximum height. maximum height above ground m time to reach maximum height s (b) Repeat your calculations choosing the origin at the base of the building. maximum height above ground m time to reach maximum height sA skateboarder shoots off a ramp with a velocity of 6.7 m/s, directed at an angle of 59° above the horizontal. The end of the ramp is 1.2 m above the ground. Let the x axis be parallel to the ground, the +y direction be vertically upward, and take as the origin the point on the ground directly below the top of the ramp. (a) How high above the ground is the highest point that the skateboarder reaches? (b) When the skateboarder reaches the highest point, how far is this point horizontally from the end of the ramp?During volcanic eruptions, chunks of solid rock can be blasted out of the volcano; these projectiles are called volcanic bombs. The figure shows a cross section of Mt. Fuji, in Japan. (a) At what initial speed would a bomb have to be ejected, at angle 0o = 41° to the horizontal, from the vent at A in order to fall at the foot of the volcano at B, at vertical distance h = 3.20 km and horizontal distance d = 9.70 km? Ignore, for the moment, the effects of air on the bomb's travel. (b) What would be the time of flight? 00 d B
- A projectile is launched from the top of the cliff of height h with initial velocity v0 and launch angle ? with respect to the horizontal. It later hits the ground. Derive an expression for the magnitude and direction angle of the velocity as the object hits the ground in terms of some or all of the variables given in the problem h, v0 , ?, and g.A skateboarder shoots off a ramp with a velocity of 7.9 m/s, directed at an angle of 51° above the horizontal. The end of the ramp is 1.4 m above the ground. Let the x axis be parallel to the ground, the +y direction be vertically upward, and take as the origin the point on the ground directly below the top of the ramp. (a) How high above the ground is the highest point that the skateboarder reaches? (b) When the skateboarder reaches the highest point, how far is this point horizontally from the end of the ramp? (a) Number_____ Units_____ (b) Number ____ Units ____A fireworks show is choreographed to have two shells cross paths at a height of 138 feet and explode at an apex of 180 feet under normal weather conditions. If the shells have a launch angle 9 = 61° above the horizontal, determine the common launch speed n for the shells, the separation distance dbetween the launch points A and B. and the time tfrom launch at which the shells explode. Determine the time t; from launch to when the paths cross. 42' 138' Vo e B d- Answer: t = sec