A long jumper uses only the run up before jumping to cover the distance. If this is the case, what is the speed that a long jumper needs to have to equal the world record of 8.95 m
A long jumper uses the run up before the actual jump to gain some momentum which is used during the actual jump. Here, an assumption has to be made that the long jumper only uses the speed after the run up to complete a jump of 8.95 m. It is assumed that the runner can change the direction of velocity acquired accurately to be able to launch herself at an angle of 45 degrees; this is the angle of launch that allows a maximum horizontal distance to be covered for the same initial velocity.
When an object is projected with velocity v at an angle 45 degrees, the horizontal distance covered is equal to `D = v^2/g`
Substituting D = 8.95 m and g = 9.8 m/s^2 gives: `v^2 = 8.95*9.8`
=> `v = sqrt(8.95*9.8)`
=> v = 9.365 m/s
With the assumptions made as required in the problem, the athlete would have to acquire a speed of 9.365 m/s to be able to complete the jump of 8.95 m