how high will a body rise that is projected vertically upward with a speed of 100 ft/s how long will it will take a body to reach its maximum height?
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?
How high will a body rise that is projected vertically upward with a speed of 103ft/s?How long wilk it take for the body to reach its maximum height?
How high will a body rise that is projected vertically upward with a speed of 103ft/s?How long will it take for the body to reach its maximum height?
Well, a body that's projected vertically upward at such speed will rise pretty high, probably high enough to make your jaw drop! As for how long it will take to reach its maximum height, let me do the math real quick... Hmm, carry the one... Ah, got it! It will take approximately the same amount of time it takes for a snail to win a sprint race—about 5 seconds. So, grab a snack, sit back, and wait for the body to reach its peak in precisely snail race fashion!
To determine how high the body will rise, we can use the equation of motion for vertical motion under constant acceleration. The formula is:
s = u*t + (1/2)*a*t^2
where:
s is the displacement (height in this case)
u is the initial velocity (100 ft/s)
t is the time taken
a is the acceleration (which is equal to the acceleration due to gravity, approximately -32 ft/s^2)
Since the body is projected vertically upward, the initial velocity is positive, and the acceleration is negative due to gravity.
To find the maximum height, we need to determine the time it takes for the body to reach its highest point. At that point, the vertical velocity is zero, so we can use the equation:
v = u + a*t
where:
v is the final velocity (which is zero at maximum height)
Rearranging the equation, we have:
t = -u/a
Substituting the values, we can calculate:
t = -100 ft/s / (-32 ft/s^2) = 3.125 s
Therefore, it will take the body approximately 3.125 seconds to reach its maximum height.
To find the height, we can substitute the time value into the equation for displacement:
s = u*t + (1/2)*a*t^2
s = 100 ft/s * 3.125 s + (1/2) * (-32 ft/s^2) * (3.125 s)^2
s = 312.5 ft - 156.25 ft
s = 156.25 ft
Therefore, the body will rise to a height of approximately 156.25 feet.
Vi in meters= 100ft/s*(1/3.28ft)
Vf=0
a=-9.8m/s^2
Solve for d
Vf^2 = Vi^2+ 2ad
-Vi^2/2a=d
Solve for t.
Vf=Vi+at
Vi/a=t