The speed of a projectile when it reaches its maximum height is 0.42 times its speed when it is at half its maximum height. What is the initial projection angle of the projectile?

Consider a projectile being launched with an initial speed of 43 m/s at a variety of initial angles. Refer to the figure. What is the range, in meters, of the projectile if it is launched at an angle of θ1 = 79.7°?  What is the range, in meters, of the projectile if it is launched at an angle of θ2 = 40.5°?  What is the range, in meters, of the projectile if it is launched at an angle of θ3 = 90 − 79.7°, the complement of θ1?

Consider three displacement vectors A = (3x - 3ý) m, B = (- 4y) m,and C = (-28 + 5ý) m. The magnitude and direction of D = A+ B + Č is m and _of %3D %3D O 2.8, 45, S of W O 6.3, 18, S of W O 2.8, 45, N of E O 6.3, 18, N of E

A Water Balloon Battle. You are launching water balloons at a rival team using a large slingshot. The other team is set up on the opposite side of a flat-topped building that is 30.0 ft tall and 50.0 ft wide. Your reconnaissance team has reported that the opposition is set up 10.0 m from the wall of the building. Your balloon launcher is calibrated for launch speeds that can reach as high as 100 mph at angles between 0 and 85.0° from the horizontal. Since a direct shot is not possible (the opposing team is on the opposite side of the building), you plan to splash the other team by making a balloon explode on the ground near them. If your launcher is located 55.0 m from the building (opposite side as the opposing team), what should your launch velocity be ((a) magnitude and (b) direction) to land a balloon 5.0 meters beyond the opposing team with maximum impact (i.e. maximum vertical speed)? (a) Number i (b) Number i Units Units

A  projectile is shot from the edge of a cliff with an initial speed of 150 m/s at an angle of 60.0° above the horizon. The cliff is located 125 m above the ground at the bottom of the cliff, which is a flat, featureless horizontal plane that extends as far as the eye can see.(a) Determine the time taken by the projectile to go from the cliff edge to the ground below the cliff. (b) Determine how far horizontally the projectile traveled from the base of the cliff. (c) Determine the velocity vector of the projectile just before it hits the ground at the bottom of the cliff. (d) Include a complete diagram of the situation.

Dr. L. and his cat Kepler are coming home from fishing. They ended their trip on the southbank of a 1200 m wide river, directly across from where Caroline is waiting to pick them upon the north bank. They are in identical boats that travel at 4 m/s (VB) on still water. Theriver is normally ‘lazy’ and flows with negligible velocity. On a calm day, if they pointed theboats north, they would cross the river in exactly 300s. However, today, the river is flowingdue east with a constant velocity (VW) of 1 m/s relative to the ground. Kepler, because shedoesn’t know better (she is a cat after all), has not taken this into account. Without payingattention, Kepler keeps the boat pointed due north for the entire trip. A) Relative to the ground, what is Kepler’s velocity? Derive an algebraic solution(in terms of VB and VW only) and then give a numerical answer (three significant figures isfine) expressed in degrees relative to due north (e.g. ‘42.3° west of north’).

A Water Balloon Battle. You are launching water balloons at a rival team using a large slingshot. The other team is set up on the opposite side of a flat-topped building that is 30.0 ft tall and 50.0 ft wide. Your reconnaissance team has reported that the opposition is set up 10.0 m from the wall of the building. Your balloon launcher is calibrated for launch speeds that can reach as high as 110 mph at angles between 0 and 85.0° from the horizontal. Since a direct shot is not possible (the opposing team is on the opposite side of the building), you plan to splash the other team by making a balloon explode on the ground near them. If your launcher is located 55.0 m from the building (opposite side as the opposing team), what should your launch velocity be ((a) magnitude and (b) direction) to land a balloon 5.0 meters beyond the opposing team with maximum impact (i.e. maximum vertical speed)? (a) Number i (b) Number i Save for Later Units Units Attempts: 0 of 1 used Submit Answer

In the middle of the night you are standing a horizontal distance of 14.0 m from the high fence that surrounds the estate of your rich uncle. The top of the fence is 5.00 m above the ground. You have taped an important message to a rock that you want to throw over the fence. The ground is level, and the width of the fence is small enough to be ignored. You throw the rock from a height of 1.60 m above the ground and at an angle of 48.0° above the horizontal. Part A What minimum initial speed must the rock have as it leaves your hand to clear the top of the fence? Express your answer with the appropriate units. % = 13.3 m S Submit Previous Answers ✓ Correct Part B For the initial velocity calculated in the previous part, what horizontal distance beyond the fence will the rock land on the ground? Express your answer with the appropriate units. d = μA Value m ?

Find the ranges shown for the projectiles in the figure for an initial speed of 50 m/s at the given initial angles. Part A: What is the range, in meters, for the projectile with the angle of 15°?  Part B: What is the range, in meters, for the projectile with the angle of 45°?  Part C: What is the range, in meters, for the projectile with the angle of 75°?