Question

A car starts from rest and accelerates at 5 m/s2. At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s​

Answer 1

Given info : A car starts from rest and accelerates at 5 m/s² . at t = 4s , a ball is dropped out of a window by a person sitting in the car.

To find : the velocity and acceleration of the ball at t = 6s, is ..

solution : initial velocity of the car, u = 0 m/s

acceleration of the car, a = 5m/s²

velocity of the car at t = 4s, v = 0 + 5 × 4 = 20 m/s [ using v = u + at ]

at the moment, when person sitting in the car dropped a ball, velocity of the ball equals the that of the car.

so, initial velocity of the ball, u = 20 m/s horizontally

acceleration acting on the ball is acceleration due to gravity [ cause it is freely falling ]

so, a = - 10m/s² downwards

at time, t = 6s - 4s = 2s

now using formula, $\vec v=\vec u+\vec a t$

= $20\hat i+(-10\hat j)(2)$ = $20\hat i-20\hat j$

now the magnitude of the velocity , v = $\sqrt{20^2+(-20)^2}=20\sqrt{2}$

therefore the velocity and acceleration of the ball are $20\sqrt{2}$ m/s and 10 m/s² respectively.

Answer 2

Answer:

Given: A car starts from rest and accelerates at 5 m/s². At t=4s, a ball is dropped out of a window.

To find: The velocity and acceleration of the ball at t=6s.

Solution:

To find the velocity of the car at t = 4s, we use the formula,

       

Here, v is the final velocity of the car, u is the initial velocity of the car, a is the aaceleration of the care and t is the time.

Let the velocity of the ball due to the car be equal to ,

       

       

The initial velocity here, is zero because the car starts from rest.

Let the velocity of the ball due to the acceleration due to gravity be equal to .

So,

             

Here, a is replaced by g, that is, the acceleration due to gravity (10ms⁻²) and 2s is the time interval between 4s and 6s.

Hence, velocity of the ball, v,

       

         

          .

The acceleration of the ball, a,

       

       

         

Therefore, the velocity and acceleration od the ball at t = 6s is 20√2 ms⁻¹ and 10√2 ms⁻².

Explanation: