When a football team is forced to punt the ball, it is very important to kick th

Question

When a football team is forced to punt the ball, it is very important to kick the ball as far as possible but also to attain a long hang time. The ball should remain in the air long enough that the punt-coverage team has time to run down field and tackle the receiver right after the catch. What are the initial angle and speed with which a football has to be punted so that its hang time is 4.25 s and it travels a distance of 52.0 m? A jet plane traveling horizontally at 1.00 times 10^2 m/s drops a rocket from a k considerable height. (1400.0 m.) The rocket immediately fires its engines, accelerating at 25.0 m/s^2 in the x-direction while falling under the influence of gravity in the y- direction. After the rocket has fallen 1.40 km (i.e. hit the ground), find (a) its velocity in the y-direction, (b) its velocity in the x-direction, and (c) the relative position of the rocket released to hit the ground in x-coordinate.

Explanation / Answer

given,

time of flight = 4.25 sec

horizontal range = 52 m

time of flight = 2 * v * sin(theta) / g

4.25 = 2 * v * sin(theta) / 9.8 ---------(1)

horizontal range = v^2 * sin(2 * theta) / g

52 = v^2 * sin(2 * theta) / 9.8 ----------(2)

on solving equation 1 and 2 we'll get

speed v = 24.15 m/s

initial angle theta = 59.56 degree

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