An arrow is fired with initial velocity v0 at an angle ? from the top of battlements, a height h above the ground. (Assume ? is measured above the horizontal.) (a) In terms of h, v0, ?, and g, what is the time at which the arrow reaches its maximum height? t=? (b) In terms of h, v0, ?, and g, what is the maximum height above the ground reached by the arrow? hmax = ?

A high-performance jet plane, practicing radar avoidance maneuvers, is in horizontal flight 40.0 m above the level ground. Suddenly, the plane encounters terrain that slopes gently upward at 3.90°, an amount difficult to detect (see the figure). How much time does the pilot have to make a correction to avoid flying into the ground ( s)? The speed of the plane is 1200 km/h.

The initial speed of a tennis ball is 57.5 m/s and the launch angle is ?i = 16°. Neglect air resistance.Question 1) What is the maximum height, h, of the tennis ball? in mQuestione 2) What is the range, R, of the tennis ball? in m info given: what angle results in the greatest height=90 For this 90° angle, the horizontal component of velocity is zero, so the initial velocity is completely in the vertical direction, resulting in greatest height Kato tries substituting ty,max for t, 0 for yi, and h for yf, and gets h =  vi2 sin2 ?i 2g   When ?i = 90°, sin2 ?i is maximum, so h is maximum what angle results in the maximum horizontal range=45°  I substituted 2vi sin ?i g into the expression for the horizontal component of velocity, (vi cos ?i)t, and got  R =  2vi2 sin ?i cos ?i g when ?i = 45°, 2?i = 90°, and sin 90° = 1, which is its maximum value.

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).

An object is launched at a velocity of 20m/s in a direction making an angle of 25° upward with the horizontal. a) What is the maximum height reached by the object? b) What is the total flight time ( between launch and touching the ground) of the object? C) What is the horizontal range (maximum x above ground) of the object? d) What is the magnitude of the velocity of the object just before it hits the ground?

An object on the ground is launched at 35ˍm/s at an angle of 61° above the horizontal. If the object lands on top of a 5.9ˍm tall hill, then what is the horizontal displacement of the object?

Please answer the following. If not then answer number 3 only.