How high will a body rise that is projected vertically upward with a speed of 100 ft/s?
How long will it take for the body to reach its maximum height?
g = 32 ft/s^2 ... so time to peak is ... (100 ft/s) / (32 ft/s^2) = ?
initial K.E. equals peak P.E.
... 1/2 m v^2 = m g h
... h = v^2 / (2 g) = 100^2 / (2 * 32) = ?
To determine the maximum height the body will reach, we can use the kinematic equation for vertical motion:
h = (v^2) / (2g)
where:
h = maximum height
v = initial velocity
g = acceleration due to gravity (32.2 ft/s^2)
Substituting the given values:
h = (100^2) / (2*32.2)
h ≈ 156.52 ft
Therefore, the body will rise to a maximum height of approximately 156.52 ft.
To calculate the time it takes for the body to reach its maximum height, we can use another kinematic equation:
v = u - gt
where:
v = final velocity (0 ft/s at maximum height)
u = initial velocity (100 ft/s)
g = acceleration due to gravity (32.2 ft/s^2)
t = time
Rearranging the equation:
t = (u - v) / g
t = (100 - 0) / 32.2
t ≈ 3.11 seconds
Therefore, it will take approximately 3.11 seconds for the body to reach its maximum height.
To find out how high the body will rise when projected vertically upward with a speed of 100 ft/s, we can use the equation of motion for vertical motion.
The equation is:
h = (v^2 - u^2) / (2 * g)
where:
h is the height,
v is the final velocity (0 ft/s at maximum height),
u is the initial velocity (100 ft/s),
g is the acceleration due to gravity (32.2 ft/s^2).
Substituting the given values into the equation, we get:
h = (0^2 - 100^2) / (2 * 32.2)
h = (-10,000) / 64.4
h ≈ -155.28 ft
The result comes out as a negative value because the equation assumes upward motion as positive and downward motion as negative. So, the body will rise approximately 155.28 ft.
Next, to find the time it takes for the body to reach its maximum height, we can use the equation of motion:
v = u - g * t
where:
v is the final velocity (0 ft/s at maximum height),
u is the initial velocity (100 ft/s),
g is the acceleration due to gravity (32.2 ft/s^2),
t is the time taken.
Rearranging the equation to solve for time, we get:
t = (v - u) / g
Substituting the given values, we have:
t = (0 - 100) / 32.2
t = -100 / 32.2
t ≈ -3.11 s
Again, the result is negative because the equation assumes upward motion as positive and downward motion as negative. Thus, it will take approximately 3.11 seconds for the body to reach its maximum height.