Problem 1: A toy cannon launches pellets (projectiles) at a muzzle velocity vo=7m/s. Gravity acceleration is g=-9.8m/s². The angle of inclination at which the cannon launches the projectiles (hereafter denoted α) can be controlled. Assume that the target (a small paper boat) is placed at the maximum distance that the cannon can reach and that the angle a is chosen precisely so that the range is maximum (see Figure below), then calculate: a) The time it takes for the projectile from exiting the cannon to impact with the ship. Option A: 1.01 s Option B: 12.00 s Option C: 3.33 s Option D: 0.25 s b) The distance the ship is from the cannon. Option A: 1 m Option B: 5 m Option C: 0.5 m Option D: 12 m c) The maximum height, h, that the projectile reaches, i.e. the apex Option A: 1.25 m Option B: 5m Option C: 0.5 m Option D: 3 m d) The time it takes for the projectile to reach the maximum height. Option A: 2 s Option B: 0.51 s Option C: 1 s Option D: 3.33 s e) The velocity vector at the moment the projectile is at the apex. Option A: 121 m/s Option B: (0, 0) m/s Option C: (2.45 m/s, 2.45 m/s) Option D: (4.95 m/s, 0)

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).

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.

A particle moving in the x-y plane has a position vector given by r- 1.67t2i+1.44t³j, where r is in inches and t is in seconds. Calculate the radius of curvature p of the path for the position of the particle when t- 1.9 sec. Sketch the velocity v and the curvature of the path for this particular instant. Answer:p-i in.

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 ?