A body is thrown up with a velocity of 78.4m/s.find how height will with rise and how much time if it take to return its point of rejection?
To find the height the body will rise and the time it will take to return to its point of projection, we can use the equations of motion for vertical motion under constant acceleration.
Given:
Initial velocity (u) = 78.4 m/s
Acceleration due to gravity (g) = 9.8 m/s^2 (assuming the motion is on Earth's surface)
Final velocity (v) at the highest point is 0 m/s since the body momentarily comes to rest at the highest point.
We need to find:
1. The height (h) the body will rise
2. The time (t) it will take to return to its point of projection
Step 1: Find the time taken to reach the highest point using the equation v = u + gt, where v = 0 m/s:
0 = 78.4 - 9.8t
9.8t = 78.4
t = 78.4 / 9.8
t ≈ 8 seconds
Step 2: Calculate the height using the equation h = ut + (1/2)gt^2:
h = (78.4 × 8) + (0.5 × 9.8 × 8^2)
h = 627.2 + 0.5 × 9.8 × 64
h = 627.2 + 313.6
h ≈ 940.8 meters
Therefore, the body will rise to a height of approximately 940.8 meters and it will take around 8 seconds to return to its point of projection.
To find the height the body will rise and the time it takes to return to its point of projection, we need to use the equations of motion.
The equation we will use to find the height the body will rise is the vertical displacement formula:
h = (v^2 - u^2) / (2 * a)
Where:
h is the height the body will rise
v is the final velocity (0 m/s at the highest point)
u is the initial velocity (78.4 m/s)
a is the acceleration due to gravity (-9.8 m/s^2)
Substituting the given values into the equation:
h = (0^2 - 78.4^2) / (2 * (-9.8))
h = (0 - 6147.36) / (-19.6)
h = -6147.36 / -19.6
h ≈ 313.84 meters
So, the body will rise to a height of approximately 313.84 meters.
To find the time it takes to return to its point of projection, we can use the formula:
t = (v - u) / a
Where:
t is the time taken
v is the final velocity (0 m/s at the highest point)
u is the initial velocity (78.4 m/s)
a is the acceleration due to gravity (-9.8 m/s^2)
Substituting the given values into the equation:
t = (0 - 78.4) / (-9.8)
t = -78.4 / -9.8
t ≈ 8 seconds
So, it will take approximately 8 seconds for the body to return to its point of projection.
the free fall equation is
... h = -4.9 t^2 + 78.4 t
max t is on the axis of symmetry
... t = -78.4 / (2 * -4.9)
find max t and plug into free fall equation to find max height
time up equals time down, so the flight time is twice max t
a. V^2 = Vo^2 + 2g*h.
0 = (78.4)^2 - 19.6h, h = ?.
b. V = Vo + g*Tr. Tr = Rise time.
0 = 78.4 - 9.8Tr, Tr = ?.
Tf = Tr. Tf = Fall time.
Tr + Tf = Time in flight.