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A rocket is launched vertically into the air and falls to the ground 15 seconds later. Determine the maximum height of the rocket.

Answer :

To find the maximum height of the rocket, we calculate the initial velocity with the given time and gravity, then use this to determine the height using the kinematic equations for uniformly accelerated motion.

To determine the maximum height of a rocket shot vertically into the air, we use the kinematic equations for uniformly accelerated motion. Since the rocket falls back to the ground in 15 seconds, the time it takes to reach its maximum height is half of that, which is 7.5 seconds (assuming upward and downward travel times are equal).

The formula to use is H = V_i * t + (1/2) * g * t^2, where H is the height, V_i is the initial velocity, g is the acceleration due to gravity (approximately -9.81 m/s^2), and t is the time. Since the rocket falls back to the ground, its initial velocity would be positive, and upon reaching maximum height, the final velocity is 0 m/s.

To find the initial velocity (V_i), we can rearrange the formula to V_i = H/t - (1/2) * g * t. Plugging in the values, we get V_i = 0 - (1/2) * (-9.81) * (7.5^2), which gives us the initial velocity. Now, using this velocity, we can find the maximum height H using the first formula. Multiplying the initial velocity by the time and adding the product of the acceleration due to gravity and time squared.

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