At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

A ball of mass [tex][tex]$0.5 \, \text{kg}$[/tex][/tex] is released from rest at a height of [tex][tex]$30 \, \text{m}$[/tex][/tex]. How fast is it going when it hits the ground? Acceleration due to gravity is [tex][tex]$g = 9.8 \, \text{m/s}^2$[/tex][/tex].

A. [tex]31.2 \, \text{m/s}[/tex]
B. [tex]24.2 \, \text{m/s}[/tex]
C. [tex]8.6 \, \text{m/s}[/tex]
D. [tex]3.1 \, \text{m/s}[/tex]


Sagot :

To determine the speed of the ball when it hits the ground after being released from a height of 30 meters, we need to use the principles of physics, specifically the equations of motion under constant acceleration due to gravity.

Given:
- Mass of the ball, [tex]\( m = 0.5 \, \text{kg} \)[/tex]
- Height from which the ball is released, [tex]\( h = 30 \, \text{m} \)[/tex]
- Acceleration due to gravity, [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
- Initial velocity, [tex]\( u = 0 \, \text{m/s} \)[/tex] (the ball is released from rest)

The formula we use to find the final velocity ([tex]\( v \)[/tex]) of an object under free fall is derived from the kinematic equation:
[tex]\[ v^2 = u^2 + 2gh \][/tex]

Since the initial velocity [tex]\( u \)[/tex] is 0, this simplifies to:
[tex]\[ v^2 = 2gh \][/tex]

Now, substituting the given values for [tex]\( g \)[/tex] and [tex]\( h \)[/tex]:
[tex]\[ v^2 = 2 \times 9.8 \, \text{m/s}^2 \times 30 \, \text{m} \][/tex]

[tex]\[ v^2 = 588 \, \text{m}^2/\text{s}^2 \][/tex]

To find the final velocity [tex]\( v \)[/tex], we take the square root of both sides:
[tex]\[ v = \sqrt{588 \, \text{m}^2/\text{s}^2} \][/tex]

[tex]\[ v \approx 24.24871130596428 \, \text{m/s} \][/tex]

Thus, after considering the precision and rounding to one decimal place, the final velocity of the ball when it hits the ground is approximately [tex]\( 24.2 \, \text{m/s} \)[/tex].

So, the correct answer is:
[tex]\[ \boxed{24.2 \, \text{m/s}} \][/tex]

Therefore, the answer is:
B. [tex]\( 24.2 \, \text{m/s} \)[/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.