Question

If h = 3.71 meters and L = 2.06 meters, the man must run horizontally off the ledge with a minimum speed of m/s in order to land on the other side of the river. Which of the following options provides the correct minimum speed?

A) 1.00 m/s
B) 2.00 m/s
C) 3.00 m/s
D) 4.00 m/s

Answer 1

To find the minimum speed to jump a 2.06-meter-wide river from a 3.71-meter-high ledge, projectile motion equations indicate a minimum speed of approximately 2.37 m/s, which suggests option C) 3.00 m/s is the closest correct answer.

Step-by-step explanation:

To determine the minimum speed at which a man must run horizontally off a ledge of height h = 3.71 meters to land on the other side of a river that is L = 2.06 meters wide, we can use the principles of projectile motion. The time t it takes for the man to fall the 3.71 meters can be found using the equation of motion for free fall, t = √(2h/g), where g is the acceleration due to gravity (9.8 m/s²). Once t is known, we can calculate the required horizontal speed v using the formula v = L/t.

If we apply these formulas:

1. Calculate t: t = √(2*3.71/9.8) ≈ 0.869 seconds.
2. Calculate minimum speed v: v = 2.06 / 0.869 ≈ 2.37 m/s.

Since none of the options A) 1.00 m/s, B) 2.00 m/s, C) 3.00 m/s, D) 4.00 m/s exactly match this calculation, the nearest minimum speed is 2.37 m/s which means option C) 3.00 m/s would be the safest choice to ensure the man clears the 2.06-meter gap.