Question

A rocket is launched at an angle of 57.2° above the horizon with an initial speed of 75 m/s. It moves for 25 s along its initial line of motion with an acceleration of 33.5 m.s². At 25 s, the engines fail and the rocket proceeds to move as a freely falling body.

a. What is the rocket's apex altitude?
b. What is the rocket's total time in flight?
c. What is the range of the rocket?

Answer 1

To find the rocket's apex altitude, use the kinematic equation and plug in the values. To find the total time in flight, double the time it takes to reach the highest point. To find the range, multiply the initial speed by the total time in flight.

Step-by-step explanation:

To find the rocket's apex altitude, we first need to determine the time it takes for the rocket to reach its highest point. Since the rocket moves with an acceleration along its initial line of motion for 25 s, and then moves as a freely falling body, we can find the time it takes to reach the highest point by dividing the total time of flight (T) by 2. In this case, T is 25 s, so the time to reach the highest point is 12.5 s.

Now, we can use the kinematic equation to find the apex altitude (h). The equation is given by h = v0t - (1/2)gt2, where v0 is the initial speed of the rocket, t is the time to reach the highest point, and g is the acceleration due to gravity. Plugging in the values, we get h = (75 m/s)(12.5 s) - (1/2)(9.8 m/s²)(12.5 s)2. Calculating this will give us the rocket's apex altitude.

To find the rocket's total time in flight, we can simply double the time it took to reach the highest point. So the total time in flight is 2(12.5 s) = 25 s.

To find the range of the rocket, we use the formula R = v0t, where R is the range, v0 is the initial speed, and t is the total time in flight. Plugging in the values, we get R = (75 m/s)(25 s). Calculating this will give us the range of the rocket.