Question

A rocket is fired at 100 m/s at an angle of 37, how many seconds did it take to get to the top?

Answer 1

Answer:

6.14 s

Explanation:

The time the rocket takes to reach the top is only determined from its vertical motion.

The initial vertical velocity of the rocket is:

$u_y = u sin \theta = (100)(sin 37^{\circ})=60.2 m/s$

where

u = 100 m/s is the initial speed

$\theta=37^{\circ}$ is the angle of launch

Now we can apply the suvat equation for an object in free-fall:

$v_y = u_y +gt$

where

$v_y$ is the vertical velocity at time t

$g=-9.8 m/s^2$ is the acceleration of gravity

The rocket reaches the top when

$v_y =0$

So by substituting into the equation, we find the time t at which this happens:

$t=-\frac{u_y}{g}=-\frac{60.2}{-9.8}=6.14 s$