Question

A ball moving at 11 m/s makes an off-center

elastic collision with another ball of equal
mass that is initially at rest. The incom-
ing ball is deflected at an angle of 29◦ from its
original direction of motion.
Find the speed of the first ball after the
collision.
Answer in units of m/s. Answer in units of
m/s

Answer 1

8.65 m/s.

Step-by-step explanation:

Let's use conservation of momentum and conservation of kinetic energy to solve this problem.

Since the two balls have equal masses, we can simplify the problem by assuming they are identical. Let's call the initial speed of the incoming ball v and the final speed of the outgoing ball v'.

Conservation of momentum tells us that the total momentum before the collision is equal to the total momentum after the collision:

mv = mv'cos(29°) + mv'sin(29°)

where m is the mass of each ball.

Conservation of kinetic energy tells us that the total kinetic energy before the collision is equal to the total kinetic energy after the collision:

(1/2)mv^2 = (1/2)mv'^2

We can solve the first equation for v' and substitute it into the second equation:

v' = v(1 - sin(29°)) / cos(29°)

(1/2)mv^2 = (1/2)m[v(1 - sin(29°)) / cos(29°)]^2

Solving for v', we get:

v' = v[1 - sin(29°)] / cos(29°)

v' = 8.65 m/s (to two decimal places)

Therefore, the speed of the first ball after the collision is 8.65 m/s.