Kinematics Model Rocket problem

[nycjay222]

Kinematics Model Rocket problem !

A) A model rocket is launched straight upward with an initial speed of 49.6 m/s. It accelerates with a constant upward acceleration of 1.83 m/s2 until its engines stop at an altitude of 155 m. What is the maximum height reached by the rocket?

B) How long after lift off does the rocket reach its maximum height?

C)How long is the rocket in the air?

 

[rock.freak667]

Homework Equations

v²=u²+2a(s-s₀)

v=u+at

s=s₀ut+1/2at²

you will need these

The Attempt at a Solution

you will need to do this

 

[tomcue]

A) To determine the maximum height reached by the rocket, we can use the kinematic equation: h = h0 + v0t + (1/2)at^2, where h is the final height, h0 is the initial height (in this case, 0 m), v0 is the initial velocity (49.6 m/s), a is the acceleration (1.83 m/s^2), and t is the time. Rearranging the equation to solve for h, we get: h = (v0^2/2a) + h0 = (49.6^2/2*1.83) + 0 = 667.5 m. Therefore, the maximum height reached by the rocket is 667.5 m.

B) To determine the time it takes for the rocket to reach its maximum height, we can use the kinematic equation: vf = v0 + at, where vf is the final velocity (in this case, 0 m/s). Rearranging the equation to solve for t, we get: t = vf/a = 0/1.83 = 0 seconds. This means that the rocket reaches its maximum height immediately after its engines stop.

C) To determine the total time the rocket is in the air, we can use the kinematic equation: vf = v0 + at, where vf is the final velocity (in this case, 0 m/s). Rearranging the equation to solve for t, we get: t = vf/a = 0/1.83 = 0 seconds. This means that the rocket is in the air for 0 seconds, as it reaches its maximum height at the same time its engines stop.