A toy rocket is launched vertically from ground level at time t = 0.00 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 64 m and acquired an upward velocity of $60 \mathrm {~m} / \mathrm { s }$ The rocket continues to rise with insignificant air resistance in unpowered flight, reaches maximum height, and falls back to the ground. The time interval during which the rocket engine provided the upward acceleration, is closest to
A)2.1 s.
B)2.3 s.
C)1.9 s.
D)1.7 s.
E)1.5 s.

Question

Quizplus · Accepted Answer

The correct answer is A.The rocket's initial velocity is 0 m/s. The rocket's final velocity at burnout is 60 m/s. The rocket's displacement at burnout is 64 m. The acceleration of the rocket is constant during the burn phase.We can use the following equation to find the time interval during which the rocket engine provided the upward acceleration:```v^2 = u^2 + 2as```where:* v is the final velocity (60 m/s)* u is the initial velocity (0 m/s)* a is the acceleration (constant during the burn phase)* s is the displacement (64 m)Substituting the given values into the equation, we get:```60^2 = 0^2 + 2a * 64```Solving for a, we get:```a = 45 m/s^2```Now we can use the following equation to find the time interval during which the rocket engine provided the upward acceleration:```v = u + at```where:* v is the final velocity (60 m/s)* u is the initial velocity (0 m/s)* a is the acceleration (45 m/s^2)* t is the time intervalSubstituting the given values into the equation, we get:```60 = 0 + 45 * t```Solving for t, we get:```t = 60 / 45 = 2.1 s```Therefore, the time interval during which the rocket engine provided the upward acceleration is closest to 2.1 s.

A Toy Rocket Is Launched Vertically from Ground Level at Time