Question

A 1.0 kg object is dropped from a height of 5 meters. Calculate the velocity of the object just before it hits the ground. (Assume no air resistance and \( g = 9.8 \, \text{m/s}^2 \))

• A. \( 5 \, \text{m/s} \)
• B. \( 10 \, \text{m/s} \)
• C. \( 15 \, \text{m/s} \)
• D. \( 20 \, \text{m/s} \)

Hint:

When an object is dropped from a height, the final velocity before it hits the ground can be found using the equation \( v^2 = u^2 + 2gh \), where \( u = 0 \) for an object dropped from rest.

Answer 1

The Correct Option is B

We are given: - Mass of the object, \( m = 1.0 \, \text{kg} \), - Height, \( h = 5 \, \text{m} \), - Gravitational acceleration, \( g = 9.8 \, \text{m/s}^2 \), - Initial velocity, \( u = 0 \, \text{m/s} \) (since the object is dropped from rest). We can use the following kinematic equation to find the velocity just before the object hits the ground: \[ v^2 = u^2 + 2gh \] Where: - \( v \) is the final velocity, - \( u \) is the initial velocity, - \( g \) is the acceleration due to gravity, - \( h \) is the height. Substituting the known values: \[ v^2 = 0^2 + 2 \times 9.8 \times 5 \] \[ v^2 = 98 \] \[ v = \sqrt{98} \approx 9.9 \, \text{m/s} \] Thus, the velocity of the object just before it hits the ground is approximately \( 10 \, \text{m/s} \).