Students in lab measure the speed of a steel ball launched horizontally from a table top to be 4.2 m/s. If the table top is 1.2 m above the floor, where should they place a 20 cm tall tin coffee can to catch the ball when it lands?

Calculate how long it takes to fall 1.0 meters.

(from 1.2 m to 20 cm above the floor)

Multiply that time by 4.2 m/s. That will be the horizontal location of the ball at that time.

To determine where to place the tin coffee can to catch the ball when it lands, we need to analyze the motion of the ball and calculate its horizontal distance traveled.

First, let's consider the horizontal motion of the ball. Since the ball is launched horizontally from the table top, it has an initial horizontal velocity and no initial vertical velocity. We can assume that there is no air resistance.

The horizontal distance traveled by the ball can be calculated using the formula:

distance = velocity × time

In this case, we know the initial horizontal velocity (4.2 m/s). However, we need to determine the time it takes for the ball to hit the ground.

To find the time, we can use the vertical motion of the ball. Since the ball only undergoes vertical motion due to the force of gravity, we can use the equation of motion for vertical motion:

vertical distance = initial vertical velocity × time + (1/2) × acceleration × time^2.

In this case, the initial vertical velocity is 0 m/s (as the ball is launched horizontally) and the acceleration due to gravity is -9.8 m/s^2 (since acceleration due to gravity acts downwards). The vertical distance is the height of the table top above the floor, which is 1.2 m.

Plugging these values into the equation, we get:

1.2 m = 0 × time + (1/2) × (-9.8 m/s^2) × time^2.

Simplifying the equation, we have:

1.2 m = (-4.9 m/s^2) × time^2.

Rearranging the equation, we get:

time^2 = (1.2 m) / (-4.9 m/s^2).

Solving for time, we find:

time ≈ √(0.2449 s^2).

Taking the square root, we have:

time ≈ 0.4949 s.

Now that we have determined the time it takes for the ball to hit the ground, we can calculate the horizontal distance traveled by the ball using the initial horizontal velocity and the time:

distance = velocity × time.

Plugging in the values, we have:

distance = 4.2 m/s × 0.4949 s.

Calculating this, we find:

distance ≈ 2.0796 m.

Therefore, the tin coffee can should be placed at a horizontal distance of approximately 2.08 meters from the edge of the table in order to catch the ball when it lands.

To determine where the students should place the tin coffee can to catch the ball when it lands, we need to analyze the motion of the ball.

First, let's consider the horizontal motion of the ball. Since the ball is launched horizontally, it will continue to move horizontally at a constant velocity throughout its trajectory. Therefore, the horizontal distance traveled by the ball will be the same as the horizontal distance from the table edge to the coffee can.

Using the horizontal distance formula:

Horizontal distance = horizontal velocity x time

We know that the horizontal velocity of the ball is 4.2 m/s. However, we need to determine the time it takes for the ball to reach the coffee can.

To do this, we will use the vertical motion of the ball. In this case, the ball is subjected to free fall due to gravity, which only affects its vertical motion.

The time it takes for the ball to fall from the table to the floor can be calculated using the equation:

Vertical distance = 0.5 x gravity x time^2

In this case, the vertical distance is the height of the table (1.2 m). The acceleration due to gravity on Earth is approximately 9.8 m/s^2. Plugging in these values, we can solve for time:

1.2 m = 0.5 x 9.8 m/s^2 x time^2

Simplifying the equation:

time^2 = (2 x 1.2 m) / 9.8 m/s^2
time^2 = 0.2449 s^2
time ≈ 0.495 s

Now that we have the time it takes for the ball to fall, we can calculate the horizontal distance using the known horizontal velocity:

Horizontal distance = horizontal velocity x time
Horizontal distance = 4.2 m/s x 0.495 s
Horizontal distance ≈ 2.079 m

Therefore, the students should place the tin coffee can at a horizontal distance of approximately 2.079 m from the table edge to catch the ball when it lands.