A person initially at rest throws a ball upward at an angle θ0 with an initial speed v0. He
tries to catch up to the ball by accelerating with a constant acceleration a for a time
interval ∆t1 and then continues to run at a constant speed for a time interval ∆t2. He
catches the ball at exactly the same height he threw the ball. Let g be the gravitational
constant. What was the person’s acceleration a ?
A person initially at rest throws a ball upward at an angle θ0 with an initial speed v0. He
tries to catch up to the ball by accelerating with a constant acceleration a for a time
interval ∆t1 and then continues to run at a constant speed for a time interval ∆t2. He
catches the ball at exactly the same height he threw the ball. Let g be the gravitational
constant. What was the person’s acceleration a ?
2 answers
flight time (f) is ... 2 * v0 * sin(θ0) / g
... f = ∆t1 + ∆t2
distance to catch point (d) ... f * v0 * cos(θ0)
d = 1/2 a ∆t1^2 + a ∆t1 ∆t2
a = d / (1/2 ∆t1^2 + ∆t1 ∆t2)
... = 2 v0^2 * sin(θ0) * cos(θ0) / [g (1/2 ∆t1^2 + ∆t1 ∆t2)]
... f = ∆t1 + ∆t2
distance to catch point (d) ... f * v0 * cos(θ0)
d = 1/2 a ∆t1^2 + a ∆t1 ∆t2
a = d / (1/2 ∆t1^2 + ∆t1 ∆t2)
... = 2 v0^2 * sin(θ0) * cos(θ0) / [g (1/2 ∆t1^2 + ∆t1 ∆t2)]
1 answer