a body is thrown vertically up with a initial velocity of 60 m/s. at what time it will be at the height of 100m
Answers
GIVEN:-
☢️ Initial Velocity (u) = 60m/s
☢️ Acceleration Due to Gravity = -10m/s²
☢️ Height = 100m.
To Find:-
The time taken by body to reach the Height of 100m.
Formulae Used:-
- S = ut + ½a × t²
Where,
S = Height
u = Initial Velocity
a = Acceleration
t = Time taken.
Now,
S = ut + ½ × a × t²
100 = 60×t + ½ × -10 × t²
100 = 60t -5t²
5t² - 60t +100 = 0
5t²- 50t - 10t + 100 = 0
5t(t - 10) - 10(t - 10) = 0
Or,
t - 10 = 0 , t = 10s.
5t - 10 = 0, t = 2s.
Hence, by seeing the Velocity we can conclude that body must have taken 2s. to reach the 100m.
Answer:
2 or 10 sec
Explanation:
Given; initial velocity is 60 m/s, acceleration due to gravity is -10 m/s² (as it's against the motion) and height is 100 m.
To find: Time
Using the second equation of motion,
s = ut + 1/2 at²
Substitute the values,
→ 100 = 60(t) + 1/2 (-10)t²
→ 100 = 60t - 5t²
→ 5t² - 60t + 100 = 0
→ t² - 12t + 20 = 0
Split the middle term
→ t² - 10t - 2t + 20 = 0
→ t(t - 10) - 2(t - 10) = 0
→ (t - 2) (t - 10) = 0
→ t = 2, 10
Hence, the body will be at height 100 m after 2 or 10 sec.