Answer :
To determine the final velocity of a body dropped from a tower, we can use one of the equations of motion. The equation that relates initial velocity (u), acceleration (a), time (t), and final velocity (v) is:
[tex]\[ v = u + a \cdot t \][/tex]
Here:
- [tex]\( u \)[/tex] is the initial velocity
- [tex]\( a \)[/tex] is the acceleration (which in this case will be due to gravity, [tex]\( g \)[/tex])
- [tex]\( t \)[/tex] is the time taken to reach the ground
Given:
- Initial velocity, [tex]\( u = 5 \, \text{m/s} \)[/tex]
- Acceleration due to gravity, [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
- Time, [tex]\( t = 2 \, \text{seconds} \)[/tex]
We substitute these values into the equation:
[tex]\[ v = 5 \, \text{m/s} + 9.8 \, \text{m/s}^2 \cdot 2 \, \text{seconds} \][/tex]
[tex]\[ v = 5 \, \text{m/s} + 19.6 \, \text{m/s} \][/tex]
[tex]\[ v = 24.6 \, \text{m/s} \][/tex]
Therefore, the final velocity of the body when it reaches the ground is:
[tex]\[ v = 24.6 \, \text{m/s} \][/tex]
Given the options:
a. 20 m/s
b. 15 m/s
c. 25 m/s
d. 0 m/s
None of the provided options exactly matches our calculated final velocity. However, the correct final velocity, based on our calculation, is [tex]\( 24.6 \, \text{m/s} \)[/tex].
[tex]\[ v = u + a \cdot t \][/tex]
Here:
- [tex]\( u \)[/tex] is the initial velocity
- [tex]\( a \)[/tex] is the acceleration (which in this case will be due to gravity, [tex]\( g \)[/tex])
- [tex]\( t \)[/tex] is the time taken to reach the ground
Given:
- Initial velocity, [tex]\( u = 5 \, \text{m/s} \)[/tex]
- Acceleration due to gravity, [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
- Time, [tex]\( t = 2 \, \text{seconds} \)[/tex]
We substitute these values into the equation:
[tex]\[ v = 5 \, \text{m/s} + 9.8 \, \text{m/s}^2 \cdot 2 \, \text{seconds} \][/tex]
[tex]\[ v = 5 \, \text{m/s} + 19.6 \, \text{m/s} \][/tex]
[tex]\[ v = 24.6 \, \text{m/s} \][/tex]
Therefore, the final velocity of the body when it reaches the ground is:
[tex]\[ v = 24.6 \, \text{m/s} \][/tex]
Given the options:
a. 20 m/s
b. 15 m/s
c. 25 m/s
d. 0 m/s
None of the provided options exactly matches our calculated final velocity. However, the correct final velocity, based on our calculation, is [tex]\( 24.6 \, \text{m/s} \)[/tex].
