How much longer would this jump be?

Question

An athlete executing a long jump leaves the ground at a 35° angle and travels 6.80 m.

takeoff speed is 8.31 m/s.

If this speed were increased by just 6.0%, how much longer would the jump be?

Answer 1

The range goes like v^2--it's v^2/g sin (2 theta) IIRC

So if v goes to 1.06 v,

then v^2 goes to (1.06 v)^2.

So the range goes up by almost 12%.

You don't have to worry about what the initial angle and speed and range were. All you need to know is that range goes like v^2, v goes up 6%, so range goes up almost 12%.

Answer 2

The range is proportional to square of speed at constant angle of projection. So the range would increase by 1.06x1.06 that is 1.12 times hence there would be 12 % increase in the length of the jump which is 0.12x8.37 = o.9972 m or almost 1 m.