A ball is thrown horizontally off the top of a 67 m tall building at a velocity of 7.3 m/s. How far did the ball land from the base of the building? Round your answer to 2 decimal places.

Compute the time it takes the ball to fall 67 m, and then multiply that by 7.3 m/s.

To solve this problem, we can use the equation of motion for horizontal motion:

Distance = Velocity × Time

In this case, the ball is thrown horizontally, so its initial vertical velocity is 0 m/s. This means the ball will only experience vertical acceleration due to gravity (9.8 m/s^2), and its time of flight will be the same as for an object falling freely from rest.

The time of flight can be calculated using the equation:

Time = sqrt(2 × height / acceleration due to gravity)

Substituting the given values:

Time = sqrt(2 × 67 m / 9.8 m/s^2)
Time ≈ sqrt(2 × 6.84)
Time ≈ sqrt(13.68)
Time ≈ 3.70 s (rounded to 2 decimal places)

Now, we can calculate the horizontal distance traveled by the ball:

Distance = Velocity × Time
Distance = 7.3 m/s × 3.70 s
Distance ≈ 26.91 m (rounded to 2 decimal places)

Therefore, the ball will land approximately 26.91 meters from the base of the building.

To find the distance the ball lands from the base of the building, we can use the equation of motion:

d = vt

Where:
d is the distance,
v is the horizontal velocity of the ball,
and t is the time it takes for the ball to reach the ground.

Since the ball is thrown horizontally, there is no vertical acceleration acting on it, so it will take the same amount of time to reach the ground as it would if it were simply dropped vertically from the same height.

To find the time it takes for an object to fall from a certain height, we can use the equation of motion for vertical motion:

h = (1/2)gt^2

Where:
h is the height of the building (67 m),
g is the acceleration due to gravity (9.8 m/s^2),
and t is the time.

We can rearrange the equation to solve for t:

t = sqrt(2h/g)

t = sqrt(2 * 67 / 9.8)

t = sqrt(4 * 67 / 9.8)

t = sqrt(268 / 9.8)

t = sqrt(27.35)

t ≈ 5.23 seconds (rounded to two decimal places)

Now that we know the time it takes for the ball to reach the ground, we can calculate the horizontal distance using the formula:

d = vt

d = 7.3 m/s * 5.23 s

d ≈ 38.10 meters (rounded to two decimal places)

Therefore, the ball lands approximately 38.10 meters from the base of the building.