Question

A body is thrown vertically upwards and rises to a height of 10 m. The time taken by the body to reach the highest point is; $(g=9.8m/s^2)$

• A. 1.41 s
• B. 4.1 s
• C. 1.24 s
• D. None of these

Answer 1

The correct option is A

1.41 s

Step 1: Given data

1. The body is thrown upwards.
2. The body rises to a height of 10 m.

Now we know that;

1. The final velocity of the body at the highest point will be zero.
2. Acceleration due to gravity will be negative as the body is moving upward and we are taking an upward direction as positive, i.e. -9.8 m/s².

Step 2: Finding initial velocity

From the 3^rd equation of motion,

$v^2-u^2=2as$

Where v and u are final and initial velocities respectively, ‘a’ is a constant acceleration, and s is displacement.

$$\begin{gathered} 0-u^2=2\times (-9.8)\times 10 \\ -u^2=-196 \\ {u}^2=\sqrt{196} \\ u=\pm 14m/s. \end{gathered}$$

Now here as we are throwing the body upward and an upwards direction we are taking as positive so we will take the positive value of u.

$u=14m/s.$

Step 3: Finding time taken by the body

Considering 1^st equation of motion,

$v=u+at$

Where v and u are the final and initial velocities, ‘a’ is a constant acceleration, and t is time.

$$\begin{gathered} 0=14-9.8\left(t\right) \\ t=\frac{14}{9.8} \\ t=1.41s \end{gathered}$$

Therefore, the time taken by the body to reach the highest point is 1.41 s.

Hence, the correct option is (A).