A skydiver competing for an Olympic gold medal jumps a horizontal distance of 135 meters. The takeoff point of the skydiver is at a height of 25 meters. With what horizontal speed must she leave the jump? Group of answer choices
55 m/s
5.9 m/s
2.3 m/s
59 m/s
To solve this problem, we need to determine the horizontal speed required for the skydiver to cover a horizontal distance of 135 meters while falling from a height of 25 meters.
First, we calculate the time it takes for the skydiver to fall 25 meters vertically. We use the formula for the time of free fall:
[ t = \sqrt{\frac{2h}{g}} ]
where:
[ t = \sqrt{\frac{2 \times 25}{9.8}} ] [ t = \sqrt{\frac{50}{9.8}} ] [ t \approx \sqrt{5.102} ] [ t \approx 2.26 , \text{seconds} ]
Next, we use the horizontal distance formula to find the horizontal speed ( v ):
[ d = v \times t ]
where:
Solving for ( v ):
[ v = \frac{d}{t} ] [ v = \frac{135}{2.26} ] [ v \approx 59.73 , \text{m/s} ]
Therefore, the horizontal speed with which the skydiver must leave the jump is approximately 59.73 m/s. The closest answer choice is:
59 m/s