When a water gun is fired while being held horizontally at a height of 1.00 m above ground level, the water travels a horizontal distance of 5.30 m. A child, who is holding the same gun in a horizontal position, is also sliding down a 45° incline at a constant speed of 2.44 m/s. If the child fires the gun when it is 1.1 m above the ground and the water takes 0.3294 s to reach the ground, how far will the water travel horizontally?

Question

When a water gun is fired while being held horizontally at a height of 1.00 m above ground level, the water travels a horizontal distance of 5.30 m. A child, who is holding the same gun in a horizontal position, is also sliding down a 45° incline at a constant speed of 2.44 m/s. If the child fires the gun when it is 1.1 m above the ground and the water takes 0.3294 s to reach the ground, how far will the water travel horizontally?

Answer 1

To find the horizontal distance the water will travel, we need to calculate the time it takes for the water to travel from the child's position to the ground.

The time taken by the water to reach the ground can be found using the equation of motion:

s = ut + (1/2)at^2

Where:
s = distance traveled in the vertical direction (1.1 m - h), where h is the height above the ground when the water gun is fired.
u = initial vertical velocity (0 m/s since the water gun starts from rest)
a = acceleration due to gravity (-9.8 m/s^2)
t = time taken

Applying the equation of motion, we have:

s = ut + (1/2)at^2
1.1 - h = 0 + (1/2)(-9.8)t^2
1.1 - h = -4.9t^2

Since we know the time taken for the water to reach the ground is given as 0.3294 s, we can substitute this into the equation:

1.1 - h = -4.9(0.3294)^2
1.1 - h = -4.9(0.1083)
1.1 - h = -0.5304
h = 1.1 + 0.5304
h = 1.6304 m

So, the height above the ground when the water is fired is 1.6304 m.

Now, we need to calculate the time it takes for the water to travel horizontally. The time taken for the water to travel horizontally is the same as the time taken for the child to slide down the incline, since they both start and end at the same time and position.

Using the formula:

velocity = distance / time

We can rearrange it to find the time:

time = distance / velocity

For the child sliding down the incline:

time = 5.3 m / 2.44 m/s
time ≈ 2.17 seconds

So, the time taken for the water to travel horizontally is approximately 2.17 seconds.

Finally, we can find the horizontal distance traveled by the water by multiplying the time by the horizontal velocity of the water gun:

distance = time * horizontal velocity

distance = 2.17 s * 2.44 m/s
distance ≈ 5.29 meters

Therefore, the water will travel approximately 5.29 meters horizontally.