A stone is thrown vertically upward from the top of a tower of height 24.5m with an initial velocity of 19.6 m/s. Calculate :- ➻ (a) the height to which the stone will rise before returning to the ground ➻(b) the velocity with which it will strike the ground ➻(c) the total time of its journey.
Answers
Given :-
Initial velocity (u) = 19.6 m/s
Acceleration due to gravity (g) = 9.8 m/s
To Find :-
(a) The height to which the stone will rise before returning to the ground
(b) The velocity with which it will strike the ground
(c) The total time of its journey.
Solution :-
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✭ Solving for (a) :-
Final velocity (v) of stone is 0 m/s because it attained it's maximum position.
Now, we have final velocity (v), initial velocity (u) and acceleration due to gravity (g). So, we can easily find height by using kinematics equation.
We know that,
✪ v² = u² + 2gh ✪
Putting values in formula we get,
↦ (0)² = (19.6)² + (2 × -9.8 × h)
↦ 0 = 384.16 + (-19.6h)
↦ -384.16 = -19.6h
↦ h = -384.16/-19.6
↦ h = 384.16/19.6
➦ h = 19.6 m
∴ Height attained by stone before returning to ground is 19.6 m.
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✭ Solving for (b) :-
↪ Total height of the stone = height of tower + height of stone
↪ Total height of the stone = (24.5 + 19.6) m
➢ Total height of the stone = 44.1 m
Initial velocity (u) is 0 as stone reached it's maximum height.
We have initial velocity (u), height (h) and acceleration due to gravity (g). So, again we will use kinematics equation to find final velocity.
We know that,
✪ v² = u² + 2gh ✪
Putting values in formula we get,
⇒ v² = (0)² + (2 × 9.8 × 44.1)
⇒ v² = 0 + 864.36
⇒ v² = 864.36
⇒ v = √864.36
➠ v = 29.4 m/s
∴ Velocity with which it will strike the ground is 29.4 m/s.
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✭ Solving for (c) :-
Now, we have all values i.e, height (h), initial velocity (u) and acceleration due to gravity (g). So, we will use kinematics equation to find total time.
We know that,
✪ h = ut + ½ gt² ✪
Putting values in formula we get,
➳ 44.1 = (0 × t) + (½ × 9.8) × t²
➳ 44.1 = 0 + 4.9 × t²
➳ 44.1 = t² × 4.9
➳ t² = 44.1/4.9
➳ t² = 9
➳ t = √9
➳ t = √(3 × 3)
➲ t = 3 s
∴ Total time of it's journey is 3 seconds.
Answer:
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