Question:

A man throws a ball vertically upward and it rises through 20 m and returns to his hands. What was the initial velocity (u) of the ball and how much time (T) is remained in the air? (Take $g = 10\, m\, s^{-2}$)

Updated On: Jul 5, 2022
  • $u = 10\, m\, s^{-1},\, T = 2\, s$
  • $u = 10\, m\, s^{-1},\, T = 4\, s$
  • $u = 20\, m\, s^{-1},\, T = 2\, s$
  • $u = 20\, m\, s^{-1},\, T = 4\, s$
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The Correct Option is D

Solution and Explanation

Taking vertically upward motion of ball, we have $\upsilon^{2} = u^{2} + 2gs$ or $0 = u^{2} + 2 \times \left(-10\right)\times 20$ or $u = 20\, m \,s^{-1}$ Taking vertical motion of ball for whole flight, $S = ut + \frac{1}{2}gt^{2}$ $0 = 20\times t+\frac{1}{2}\times\left(-10\right)\times t^{2}$ $5t^{2} - 20\, t = 0 ? t = 4 \,s.$
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Notes on Motion in a straight line

Concepts Used:

Motion in a straight line

The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion. 

Types of Linear Motion:

Linear motion is also known as the Rectilinear Motion which are of two types:

  1. Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
  2. Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.