Final answer:
Using kinematic equations and the given time intervals and acceleration due to gravity, the initial velocity of the balls can be calculated. Both balls are thrown with the same initial velocity and the velocities are equal and opposite at the point of collision.
Step-by-step explanation:
The student is asking about the velocity at which two balls must be tossed vertically so that they collide in mid-air. Given that they collide 0.5 seconds after the second ball is tossed, we can use kinematic equations to find the initial velocity. The supplied acceleration due to gravity is 9.8 m/s², which will allow us to calculate the initial velocity using the equation of motion.
Let's designate the time when the first ball is tossed as t=0. The second ball is tossed at t=1 second. At t=1.5 seconds, both balls collide. For the first ball, which has been in the air for 1.5 seconds, we can use the following equation:
v1 = u - g×t
where v1 is the velocity of the first ball at the collision, u is the unknown initial velocity (the same for both balls), g is the acceleration due to gravity (9.8 m/s²) and t is the time (1.5 seconds for the first ball).
Since the balls collide, the first ball is moving downwards and the second ball upwards, so their velocities are equal in magnitude but opposite in direction. The second ball has been in the air for 0.5 seconds, so:
v2 = u - g×t
where v2 is the velocity of the second ball at the collision, and t for the second ball is 0.5 seconds.
Since v1 = -v2, we can set the equations equal to each other and solve for u:
u - g×1.5 = -(u - g×0.5)
Solving the above equation will yield the initial velocity u.