Question

You and some friends are loading a moving truck. You get a heavy box to the top of the loading ramp which is angled at 15 degrees from the ground. The high end (top) of the ramp is 12.5 m above the ground. You accidently make the assumption that your friends had the box secure and stop pushing. The box begins to move down the ramp.

How long does it take to reach the bottom of the ramp?

Answer 1

The time is
`t = 6.17 \ s`

Step-by-step explanation:

From the question we are told that

The angle is
`\theta = 15^o`

The height is
`h = 12.5 \ m`

Generally from SOHCAHTOA the length of the ramp can be evaluated as

`L = (h)/(sin (\theta))`

=>
`L = (12.5)/(sin (15))`

=>
`L = 48.3 \ m`

Generally fro kinematic equation this length is mathematically represented as

`L = ut + (1)/(2) * g* sin (\theta )t^2`

Here u = 0 m/s since the box started from rest

So

`48.3 = 0 + (1)/(2) * 9.8 * (sin(15))* t^2`

`t = \sqrt{ (2 * 48.3 )/( 9.8 * sin (15)) }`

`t =  6.17 \  s`