A ball is thrown vertically upwards with an initial velocity of 10 metre per second. calculate maximum height attained by the ball and the time taken to come back to the ground.
Answers
Answer:
Maximum height attained = 5.1 m
Total time taken = 2 s
Explanation:
Given:
- Initial velocity of the ball = 10 m/s
- Final velocity of the ball = 0 m/s
To Find:
- Maximum height attained by the ball
- Time taken to come back to the ground
Solution:
By the third equation of motion we know that,
v² - u² = 2as
Where v is the final velocity
u is the initial velocity
a is the acceleration due to gravity = -g (here g is taken as negative since the direction of motion of the ball is opposite to that of gravity)
s = maximum height reached
Substitute the data,
0² - 10² = 2 × -9.8 × s
s = -100/-19.6
s = 5.1 m
Hence the maximum height attained by the ball is 5.1 m.
Finding the total time taken by the ball to come back to the ground,
By the first equation of motion we know that
v = u + at
where a = -g
t = time taken
Substitute the data,
0 = 10 + -10t
t = 1 s
Since the ball has to travel up and down, the total time taken would be,
Time taken = 1 + 1 = 2 s
Therefore the total time taken by the ball to come back to the ground is 2 s.
Answer:
Given :-
- A ball is thrown vertically upwards with an initial velocity of 10 m/s.
To Find :-
- What is the maximum height attained by the ball.
- How much time taken to come back to the ground.
Formula Used :-
❶ To find maximum height, we know that,
✪ 2gh = v² - u² ✪
❷ To find time taken, we know that,
★ v = u + at ★
where,
- g = Acceleration due to gravity
- v = Final velocity
- u = Initial velocity
- a = Acceleration
- t = Time taken
Solution :-
❶ First, we have to find the maximum height,
Given :
- Initial velocity (u) = 10 m/s
- Final velocity (v) = 0 m/s
- Acceleration due to gravity (g) = - 9.8 m/s²
According to the question by using the formula we get,
↦ 2gh = v² - u²
↦ 2 × (- 9.8) × h = (0)² - (10)²
↦ - 19.6 × h = 0 - 100
↦ - 19.6h = - 100
↦ h = - 100/- 19.6
➠ h = 5.1 m
∴ The maximum height attained by the ball is 5.1 m .
❷ Now, we have to find the time taken to come back to the ground,
Given :
- Final velocity (v) = 0 m/s
- Initial velocity (u) = 10 m/s
- Acceleration = - 10 m/s²
According to the question by using the formula we get,
⇒ 0 = 10 + (- 10) × t
⇒ 0 = 10 - 10t
⇒ 0 - 10 = - 10t
⇒ - 10 = - 10t
⇒ - 10/- 10 = t
⇒ 1 = t
➦ t = 1 sec
Hence, the total time taken = 1 sec + 1 sec = 2 sec
∴ The time taken to come back to the ground is 2 seconds .