Question

A ball is thrown vertically up with a
velocity of 30 m/s. What is the time taken
to cover a distance of 50m by the ball?
(Take g=10m/s)
(a) 5 sec
(b) 4 sec
(c) 3 sec
(d) 2 sec​

Answer 1

Answer:

(b) 4 sec

The time taken to cover a distance of 50m by the ball is 4 seconds

$\bf\large\underline{Given :}$

• A ball is thrown vertically up with a velocity of 30m/s
• The ball covers a distance of 50m

$\bf\large\underline{To \: Find : }$

• The time taken to cover a distance of 50m by the ball .

$\bf\large\underline{Solution :}$

Given ,

Initial velocity, v = 30m/s

distance covered, s = 50m

acceleration due to gravity, g = -10m/s²

Using equations of motion we have,

$\sf\implies v^{2} - u^{2} = 2as \\\\ \sf\implies v^{2} = u^{2} + 2as \\\\ \sf\implies v^{2} = 30^{2} - 2 \times (-10)\times 50 \\\\ \sf\implies v^{2} = 900 - 1000 \\\\ \sf\implies v^{2} = -100 \\\\ \sf\implies v = -10$

Thus , final velocity is -10m/s

Again , we have

$\sf\implies a = \dfrac{v - u}{t} \\\\ \sf\implies t = \dfrac{v - u}{a} \\\\ \sf\implies t = \dfrac{-10 - 30}{-10} \\\\ \sf\implies t= \dfrac{-40}{-10} \\\\ \sf\implies t = 4$

Therefore , the time taken by the ball is 4s