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

6.14 s

Step-by-step 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=-(u_y)/(g)=-(60.2)/(-9.8)=6.14 s`