Final answer:
To determine how far a skier jumps horizontally, the time of flight was calculated using the vertical displacement due to gravity. With a horizontal velocity of 25.0 m/s and a calculated time of 0.99 seconds, the skier travels approximately 24.75 meters before landing.
Step-by-step explanation:
A student is asking how far horizontally a skier leaves the end of a horizontal ski jump at 25.0 m/s and falls 4.80 m before landing. To find the horizontal distance traveled by the skier, we can use the equations of motion for projectile motion under gravity. Since friction is neglected, the horizontal velocity of the skier remains constant at 25.0 m/s throughout the motion.
We first need to calculate the time of flight for the skier's jump to determine how long the skier will be in the air. Since the skier falls 4.80 m vertically, we can use the equation for vertical displacement under constant acceleration due to gravity (g = 9.8 m/s2).
The equation for vertical displacement is given by s = ut + 1/2 at2, where s is the vertical displacement, u is the initial vertical velocity (which is 0 m/s in this case, since the skier leaves horizontally), a is the acceleration due to gravity, and t is the time. Plugging in the values, we have:
4.80 m = 0 m/s * t + 1/2 * 9.8 m/s2 * t2
Solving for t, we get t ≈ 0.99 s.
To find the horizontal distance (d), we use the horizontal component of the velocity:
d = horizontal velocity * time = 25.0 m/s * 0.99 s ≈ 24.75 m.
Therefore, the skier travels approximately 24.75 meters horizontally before landing.