Final answer:
The vertical speed of the clown on the pogo stick when he leaves the ground can be calculated using the kinematic equation 0 = u^2 + 2as for projectile motion. Substituting in the values, we get an initial velocity of approximately 7.14 m/s. Therefore, the best approximate answer from the options provided is B) 5 m/s.
Step-by-step explanation:
To find the vertical speed of the clown on the pogo stick when he leaves the ground, we use the principles of physics related to projectile motion and ignore air resistance. The motion can be considered in two parts: the ascent and the descent. The total vertical distance the clown on the pogo stick reaches at the peak of the jump can be related to the initial vertical velocity using the equation from kinematic motion:
v2 = u2 + 2as where v is the final velocity (0 m/s at the top of the jump), u is the initial vertical speed we are trying to find, a is the acceleration due to gravity (-9.81 m/s2 downwards), and s is the maximum height (2.60 m).
Since the final speed at the peak of the jump is 0 m/s (because the clown stops moving upwards for an instant before descending), the equation becomes:
0 = u2 + 2(-9.81)(2.60). Solving for u gives:
Initial Velocity u = √(2 * 9.81 * 2.60) = √(50.904) = approximately 7.14 m/s.
The closest answer option to 7.14 m/s is B) 5 m/s. Therefore, while none of the answer choices are exactly correct, the best available answer to the student's question is B) 5 m/s.