A hammer is thrown horizontally from the flat roof of a tall building at a velocity of 10m/s and hits the ground below after 5 seconds.
(a) How high is the roof?
(b) How far from the building does it land.
a. h = 0.5g*t^2.
b. Dx = Xo*t = 10m/s * 5s. = 50 m.
To solve this problem, we can use the equations of motion for linear motion:
(a) To find the height of the roof, we need to determine the vertical displacement of the hammer as it falls. We can use the equation:
h = 0.5 * g * t^2
where h is the height of the roof, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time taken to hit the ground after being thrown horizontally.
Plugging in the values, we get:
h = 0.5 * 9.8 * 5^2
= 0.5 * 9.8 * 25
= 122.5 meters
Therefore, the height of the roof is 122.5 meters.
(b) To find the horizontal distance from the building where the hammer lands, we can use the equation:
d = v * t
where d is the distance, v is the velocity of the hammer (10 m/s), and t is the time taken to hit the ground.
Plugging in the values, we get:
d = 10 * 5
= 50 meters
Therefore, the hammer lands at a horizontal distance of 50 meters from the building.
To determine the height of the roof (part a), we need to calculate the vertical distance the hammer fell during the 5 seconds it was in the air. Since the hammer was thrown horizontally, the initial vertical velocity is 0 m/s. We can use the equation for the distance traveled in free fall:
Distance (d) = initial velocity (v) * time (t) + 0.5 * acceleration (a) * time squared (t^2)
In this case, the acceleration due to gravity (a) is -9.8 m/s^2 because it acts downward. We substitute the known values into the equation:
d = 0 * 5 + 0.5 * (-9.8 m/s^2) * (5 s)^2
d = -122.5 m
The negative sign indicates that the distance is below the starting point. However, since we are measuring the height, we take the absolute value:
Height of the roof = |d| = |-122.5 m| = 122.5 m
Therefore, the height of the roof is 122.5 meters.
To determine the horizontal distance from the building (part b), we need to calculate the horizontal displacement of the hammer during the 5 seconds it was in the air. Since the hammer was thrown horizontally, the horizontal velocity remains constant throughout the motion.
Horizontal distance (d) = initial velocity (v) * time (t)
Substituting the known values:
d = 10 m/s * 5 s
d = 50 m
Therefore, the hammer landed 50 meters away from the building.