Question

A ball is thrown vertically upward with a speed of \(19.6\ \text{m/s}\). The value of acceleration due to gravity at that place is \(9.8\ \text{m/s}^2\). The maximum height (in cm) that the ball reaches is _ _ _. (in integer)

Hint:

At the maximum height of vertical motion, the final velocity becomes zero. Use: \[ v^2=u^2-2gh \] to calculate the height reached.

Answer 1

Correct Answer: 1960

Step 1: List the data.
Launch speed $u = 19.6$ m/s, gravity $g = 9.8$ m/s$^2$, and at the top the speed is $0$.

Step 2: Pick the equation.
Use $v^2 = u^2 - 2gh$ with $v = 0$.

Step 3: Solve for height.
\[ h = \frac{u^2}{2g} = \frac{19.6^2}{2\times 9.8} = \frac{384.16}{19.6} = 19.6\ \text{m} \]

Step 4: Convert to centimetres.
Since $1$ m is $100$ cm, $19.6$ m is $1960$ cm.

Step 5: Answer.
\[ \boxed{1960\ \text{cm}} \]