# Numerical problem – a ball thrown vertically upwards

Last updated on June 13th, 2022 at 08:28 am

Here, we will Solve the following numerical problem based on the vertical motion of a ball – when a ball is thrown vertically upwards.

**Question**

**When a ball is thrown vertically upwards, it goes through a distance of 19.6 m. Find the initial velocity of the ball and the time taken by it to rise to the highest point. (Acceleration due to gravity, g=9.8 ms**^{-2}) [3 MARKS]

^{-2}) [3 MARKS]

**Solution:**

Distance traversed =s=19.6 m

say, initial velocity = u

and, say the time taken to rise to the highest point = t

We know that the velocity at the highest v = 0

Using the following equation of motion with retardation, we can find the initial velocity = u

v^{2}=u^{2}– 2gs

=> 0 = u^{2} – 2 x 9.8 x 19.6

=> u^{2}=19.6 x 19.6

**u = 19.6 m upwards**

To find out the the time taken to rise to the highest point (t) we will use the following equation:

v = u – gt

=> 0 = u – gt

**=> t = u/g = 19.6/9.8 s = 2 seconds**

**Know more about the vertical motion formulas used in this numerical problem**