The horizontal motion has no effect on the vertical drop.
From a drop, the distance the ball falls in 'T' seconds is
D = 4.9 T^2
so
2.2 = 4.9 T^2
T^2 = 2.2/4.9
T^2 = 0.449 sec^2
T = 0.67 second
What a delightful little problem !
-- When he is running on level ground, his kinetic energy is
KE = (1/2) x (mass) x (speed)² .
-- When he climbs up from the ground, his potential energy is
PE = (mass) x (gravity) x (height above the ground).
We're looking for the height that makes these quantities of energy equal,
figuring that when he runs, his speed is 11 m/s.
The first time I looked at this, I thought we would need to know the runner's
mass. But it turns out that we don't.
<u>PE = KE</u>
(mass) x (gravity) x (height) = (1/2) (mass) (11 m/s)²
Divide each side by (mass) :
(gravity) x (Height) = (1/2) (11 m/s)²
Divide each side by gravity:
Height = (1/2) (121 m²/s²) / (9.8 m/s²)
= <em>6.173 meters</em>
(about 20.3 feet !)
This is your perfect answer
The base unit for time is the second (the other SI units are: metre for length, kilogram for mass, ampere for electric current, kelvin for temperature, candela for luminous intensity, and mole for the amount of substance). The second can be abbreviated as s or sec.