A person can jump to a height of 1.5m on surface of earth. Find the velocity with which he jumps.
well, you know the equation of motion is
h(t) = vt - 4.9t^2
So, h is max at t = v/9.8
So, plug in t=v/9.8 into
vt - 4.9t^2 = 1.5
and solve for v.
To find the velocity with which a person jumps, we can use the principles of physics, specifically the laws of motion.
We will use the equation for the vertical motion of an object thrown upward:
v^2 = u^2 + 2as
Where:
v = final velocity (the velocity with which the person jumps)
u = initial velocity (which is zero since the person starts from rest)
a = acceleration due to gravity (approximately 9.8 m/s^2 on Earth, in the downward direction)
s = displacement (the height the person jumps, in this case, 1.5m)
Plugging in the given values, we get:
v^2 = 0^2 + 2 * 9.8 * 1.5
Simplifying the equation, we have:
v^2 = 2 * 9.8 * 1.5
v^2 = 29.4
To find the value of v, we take the square root of both sides:
v = √29.4
Therefore, the velocity with which the person jumps is approximately 5.42 m/s.