from the top of a multi storey building 39.2 M tall a boy projects a stone vertically upward with an initial velocity of 9.8 ms^1 such that it finally drops to the ground . first . when will the stone reach the ground ? second . when will it pass through the point of projection ? third . what will be its velocity before striking the ground ? take g = 9.8ms^2
Answers
The height reached by the projectile from point of projectile is:
V² = U² - 2gs
g= 9.8
U = 9.8
v= 0
0= 96.04-19.6S
19.6S
S= 96.04/19.6
S= 4.9m
The time taken to reach this height is:
t= u/g
= 9.8/9.8 = 1
Total height from the ground : 4.9 + 39.2 = 44.1
It takes 2 second to fall back to the point of projection.
The final velocity would be:
V= u+got
V= 0+9.8
V= 9.8
This is the initial velocity with which it falls from the point of projection to the ground.
Now using the formula below, we can get time it takes to fall from point of projection.
S = 39.2
S= it + 0.5gt²
39.2 = 9.8t + 4.9t²
Dividing through by 4.9
8= 2t + t²
to + 2t - 8 = 0
Solving by quadratic method we have:
The roots are : (-2,4)
t² + 4t - 2t - 8 = 0
t(t+4)-2(t+4) =0
(t+4)(t-2) = 0
t= -4 or 2
So we take 2 since it is positive
The total Time taken to reach the ground is thus:
2+2 = 4seconds
Answer: 4seconds
Hope this helps you friend
Thanks ✌️ ✌️
Answer:
Time taken to reach the ground
The height reached by the projectile from point of projectile is:
V² = U² - 2gs
g= 9.8
U = 9.8
v= 0
0= 96.04-19.6S
19.6S
S= 96.04/19.6
S= 4.9m
The time taken to reach this height is:
t= u/g
= 9.8/9.8 = 1
Total height from the ground : 4.9 + 39.2 = 44.1
It takes 2 second to fall back to the point of projection.
The final velocity would be:
V= u+got
V= 0+9.8
V= 9.8
This is the initial velocity with which it falls from the point of projection to the ground.
Now using the formula below, we can get time it takes to fall from point of projection.
S = 39.2
S= it + 0.5gt²
39.2 = 9.8t + 4.9t²
Dividing through by 4.9
8= 2t + t²
to + 2t - 8 = 0
Solving by quadratic method we have:
The roots are : (-2,4)
t² + 4t - 2t - 8 = 0
t(t+4)-2(t+4) =0
(t+4)(t-2) = 0
t= -4 or 2
So we take 2 since it is positive
The total Time taken to reach the ground is thus:
2+2 = 4seconds
Answer: 4seconds
Hope this helps !