You fire a ball with an initial speed v0 at an angle ϕ above the surface of an incline, which is itself inclined at an angle θ above the horizontal (Figure 1). (a) Find the distance, measured along the incline, from the launch point to the point when the ball strikes the incline. (b) What angle ϕ gives the maximum range, measured along the incline? Ignore air resistance. What is the initial x -component of the ball's initial velocity? Express your answer in terms of the variables v0 , θ, ϕ. What is the initial y -component of the ball's initial velocity? Express your answer in terms of the variables v0 , θ, ϕ.   You'll need to write an equation that relates x and y for points along the incline. What is this equation? Express your answer in terms of the variables x , θ, and appropriate constants, if needed.

The same projectile experiment was conducted as you did in class. A racquet ball rolls down a track, leaves the track at an initial height of 0.961m above floor, with an exit speed Vexit 1.40m/s at an angle exit 7.46°. The landing spot was repeatedly measured for ten times, and the racquet ball's horizontal range data is provided below. Data run = Landing spot (m) 1 2 0.585 0.590 3 4 0.595 0.590 5 6 0.585 0.580 7 0.580 8 = 9 10 0.585 0.580 0.575

Danielle launches a ball off of a platform of height h with velocity vo at an angle 0 above the horizontal. A wall with a ball-sized hole a height H above the floor, with H > h, is a horizontal distance L = 24.0 m away from Danielle. The difference in height between H and h is one-twelfth of L, and the square of the magnitude of the velocity, v, is three-halves of the product gL. H 1 H – h = h 3 L Determine the two values of 0 that ensure the ball passes through the hole. Submit the larger angle as 0, and the smaller angle as 02.

The banded archerfish is a species of fish that lives in mangrove estuaries in Asia and Oceania. It has a unique and highly effective hunting strategy: it shoots an incredibly precise stream of water out of its mouth at almost ten meters per second, knocking insects and other small animals into the water from nearby branches! Pom Fbug (t) Ө = Our hero, a hungry archerfish, has spotted a big, delicious bug sitting on a branch a height ħ above the surface of the water. The archerfish can shoot its water jet at a speed of vo. The archerfish wants to knock the bug sideways off of the branch, so it decides to shoot so that its water jet is moving horizontally at the moment when it strikes the bug. The final goal of this problem is to find the horizontal distance, d, from the branch, and the angle above horizontal, 0, at which archerfish should shoot. d (a) What are the position and velocity of the water droplet as a function of time and the position and velocity of the bug as a function of…

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?

A jetliner is moving at a speed of 245 m/s. The vertical component of the plane's velocity is 40.6 m/s. Given sin e = 0.165, the angle theta is equal to: Select one: O e = 10.0° e = 9.5° e = 11.5° e = 11.0° O O

A projectile is fired up an inclined plane (incline angle α) with an initial speed v0 at an angle β with respect to the horizontal (β > α) Let d denote the distance the projectile travels up the incline.a) Express d in terms of α, β, v0 and g.b) For what value of β is d maximal, and what is the maximum value of d?

A projectile is fired from a point 50 meter from a tall cliff at 75 m/sec and at angle of 50 degrees above the horizontal. It will strike the cliff at a point h above the cliff base. What is h? What is the final speed of the projectile when it hits the cliff in the problem above?

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 0 with respect to the horizontal. Let the building be 54.0 m tall, the initial horizontal velocity be 9.10 m/s, and the initial vertical velocity be 10.5 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 time to reach maximum height (b) Repeat your calculations choosing the origin at the base of the building. maximum height above ground time to reach maximum height

This problem will involve deriving a formula or two for a projectile launched from one height and angle and landing at a different height on Earth. Begin with a projectile launched at angle 0 above horizontal from a height y₁ with initial velocity Vo. The projectile lands at a point with height y₂. These are the given quantities: vo, 0, y₁, y2 and g. Construct formulae for each of the following, as. a function of given quantities the horizontal distance traveled. the maximum height reached. the time taken. the angle of impact. (find the final velocity components first).