Question

A ball is thrown upwards with a velocity of \(20\,m/s\). Find the maximum height reached \((g=10\,m/s^2)\).

• A. \(10\,m\)
• B. \(20\,m\)
• C. \(30\,m\)
• D. \(40\,m\)

Hint:

For vertical upward motion, maximum height can also be found directly using: \[ h = \frac{u^2}{2g} \] This shortcut is very useful in projectile and vertical motion problems.

Answer 1

The Correct Option is B

Concept: When a body is thrown vertically upward, its velocity gradually decreases due to the downward acceleration caused by gravity. At the maximum height, the velocity becomes zero. We use the equation of motion: \[ v^2 = u^2 - 2gh \] where
• \(u\) = initial velocity
• \(v\) = final velocity
• \(g\) = acceleration due to gravity
• \(h\) = maximum height

Step 1: Write the given values. \[ u = 20\,m/s \] \[ v = 0 \quad (\text{at maximum height}) \] \[ g = 10\,m/s^2 \]

Step 2: Substitute into the equation of motion. \[ 0^2 = 20^2 - 2(10)h \] \[ 0 = 400 - 20h \]

Step 3: Solve for \(h\). \[ 20h = 400 \] \[ h = 20 \] Thus, the maximum height reached is \[ \boxed{20\,m} \]