Question

A river is about 5.7 m wide. Suppose an athlete wants to jump "over the river" and leaps at an angle of 35 degrees with respect to the horizontal. What is the minimal initial speed that would allow them to make the jump and land on the other side?

Answer 1

The minimum initial speed required for an athlete to jump over a 5.7 m wide river at a 35-degree angle can be calculated using the kinematic equation for projectile motion, taking into account gravity and the width of the river.

Step-by-step explanation:

The student has asked a physics-related question about projectile motion. To determine the minimal initial speed that would allow an athlete to jump over a river 5.7 m wide at a 35-degree angle, we use the kinematic equations for projectile motion. The horizontal distance covered by a projectile (the range) is given by R = (v^2 sin(2θ)) / g, where v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity (9.81 m/s2). Solving for v, we find that v = √((R × g) / sin(2θ)). Therefore, the minimum initial speed needed can be calculated using the given parameters of the river width and the launch angle.