Excellent human jumpers can leap straight up to a height of 100 cm off the ground.
To reach this height, with what speed would a person need to leave the ground?
19.6
To determine the required speed to reach a height of 100 cm, we can use the principles of projectile motion. The initial speed of the jumper, when leaving the ground, can be calculated using the following equation:
v^2 = u^2 + 2as
Where:
v = final velocity (which is zero as the person reaches the maximum height)
u = initial velocity (what we're trying to find)
a = acceleration due to gravity (approximately 9.8 m/s^2)
s = displacement (vertical distance, which in this case is 100 cm or 1 meter)
Rearranging the equation, we have:
u^2 = v^2 - 2as
Plugging in the known values, we get:
u^2 = 0 - 2 * 9.8 * 1
Simplifying further:
u^2 = -19.6
Taking the square root of both sides:
u = √(-19.6)
Since the under-root term is negative, it means that the required speed to reach a height of 100 cm off the ground cannot be achieved by a person through a straight vertical jump.
To find the required speed to reach a height of 100 cm, we can use the principles of projectile motion. We need to determine the initial vertical velocity, assuming there is no initial vertical displacement.
The initial vertical velocity can be found using the equation:
v^2 = u^2 + 2as
Where:
v is the final vertical velocity (which will be 0 when the person reaches the highest point of the jump),
u is the initial vertical velocity,
a is the acceleration due to gravity (approximated as 9.8 m/s^2),
and s is the vertical displacement (in this case, 100 cm or 1 meter).
Rearranging the equation, we have:
u^2 = -2as
Plugging in the known values:
u^2 = -2 * (9.8 m/s^2) * (1 m)
u^2 = -19.6 m^2/s^2
Since we only need the magnitude of the initial velocity, we take the square root of both sides:
u = √(19.6 m^2/s^2)
u ≈ 4.43 m/s
Therefore, a person would need to leave the ground with a speed of approximately 4.43 m/s to reach a height of 100 cm.
100 cm = 1 meter
g = -9.81 m/s^2
(1/2) m v^2 = m g h
v = sqrt (2 g h)
v = sqrt (2*9.81*1)