Question

a compressed spring projects a ball horizontally in a vacuum chamber.
on the earth, the ball reaches the chamber floor 4.0m in front of the spring.
an identical experiment is done on the moon. the gravitational field strength is lower on the moon than on the earth.
the experimental results on the moon are compared with those on the earth.
which statement is correct?
a the horizontal speed is greater on the moon and the ball hits the floor 4.0m in front of the spring.
b the horizontal speed is greater on the moon and the ball hits the floor more than 4.0m in front of the spring.
c the horizontal speed is the same on the moon and the ball hits the floor 4.0m in front of the spring.
d the horizontal speed is the same on the moon and the ball hits the floor more than 4.0m in front of the spring.

Explanation:

Step1: Analyze horizontal motion

In horizontal direction, there is no acceleration (in vacuum, no air resistance). According to \(v = \frac{x}{t}\), and \(x = v_{0x}t\), where \(v_{0x}\) is the initial horizontal speed. Since there is no force acting on the ball in the horizontal direction in both cases (Earth and Moon), by Newton's first law, the horizontal speed \(v_{0x}\) remains constant. So the horizontal speed is the same on the Moon and on the Earth.

Step2: Analyze vertical motion

In vertical direction, \(h=\frac{1}{2}gt^{2}\), where \(h\) is the height of the vacuum chamber (constant), \(g\) is the gravitational - acceleration. On the Moon \(g_{Moon}t_{Earth}\).

Step3: Analyze horizontal displacement

Since \(x = v_{0x}t\), \(v_{0x}\) is the same, and \(t_{Moon}>t_{Earth}\), then \(x_{Moon}=v_{0x}t_{Moon}>v_{0x}t_{Earth}=4m\)

Answer:

D. The horizontal speed is the same on the Moon and the ball hits the floor more than \(4.0\space m\) in front of the spring.