posted by Zeek on .
An athlete executing a long jump leaves the ground at a 32.5° angle and travels 7.72 m. What was the take-off speed?
If this speed were increased by just 4.9 %, how much longer would the jump be?
The formula you need to answer both questions is
Distance = Vo^2*sin(2A)/g
where A it the takeoff angle.
Deriving that formula would be a good exercise for you. You would use the trig identity sin(2A) = 2 sinA cosA.
In the first case,
Vo^2 = g*7.72m/sin65 = 83.56 m^2/s^2
Take the square root of that for Vo.
Increasing the speed by a factor 1.049 will increase the length of the jump by a factor (1.049)^2 = 1.100
(a 10.0% increase).