Question

The world long jump record is 8.95 m (Mike Powell, USA, 1991). [email protected] Treated as a projectile, what is the maximum range, in meters, obtainable by a person if he or she has a take-off speed of 9.2 m/s? Assume the motion is over level ground and the initial velocity makes an angle of 45° with the horizontal.

Answer 1

8.66 m

Step-by-step explanation:

`v_(o)` = initial speed of person = 9.2 m/s

`\theta` = Angle of launch = 45°

Consider the motion of the person along the vertical direction.

`v_(oy)` = initial speed of person =
`v_(o) Sin\theta = 9.2 Sin45 = 6.51 ms^(-1)`

`a_(y)` = acceleration due to gravity =
`- 9.8 m/s^(-2)`

`t` = time of travel

`y` = vertical displacement =
`0 m`

Using the kinematics equation that suits the above list of data, we have

`y = v_(oy) t + (0.5) a_(y) t^(2) \\0 = (6.51) t + (0.5) (- 9.8) t^(2)\\t = 1.33 s`

Consider the motion of the person along the horizontal direction.

`v_(ox)` = speed of person =
`v_(o) Cos\theta = 9.2 Cos45 = 6.51 ms^(-1)`

`X` = Horizontal distance traveled

`t` = time taken =
`1.33 s`

Since there is no acceleration along the horizontal direction, we have

`X = v_(ox) t \\X = (6.51) (1.33)\\X = 8.66 m`