An arrow is fired directly horizontal off a cliff that is 10 meters tall with a velocity of 65.5m/s.
a.how long is the arrow in the air?
b.what is the range of the arrow?
To find the answer to both questions, we need to apply the equations of projectile motion. In this case, we're dealing with motion in the horizontal direction only, as the arrow is fired directly horizontally.
a. How long is the arrow in the air?
The time of flight for an object in projectile motion can be determined by using the formula:
time of flight = (2 * initial vertical velocity) / acceleration due to gravity
In this case, the arrow is fired directly horizontally, so the initial vertical velocity is 0 m/s. The acceleration due to gravity is approximately 9.8 m/s^2.
Substituting these values into the formula:
time of flight = (2 * 0 m/s) / 9.8 m/s^2
time of flight = 0 s
Therefore, the arrow is in the air for 0 seconds. Since the arrow is fired horizontally, it falls immediately due to the force of gravity.
b. What is the range of the arrow?
The range of a projectile can be calculated using the formula:
range = horizontal velocity * time of flight
In this case, the horizontal velocity of the arrow is given as 65.5 m/s, and we already determined that the time of flight is 0 s.
Substituting these values into the formula:
range = 65.5 m/s * 0 s
range = 0 m
Therefore, the range of the arrow is 0 meters. Since the arrow falls immediately when fired horizontally, it does not travel horizontally and lands at the bottom of the cliff.