If a spring gun shoots a ball horizontally at 8 m/s, and the ball starts out 1.7 m above the floor, how far away from the gun will the ball land?
To find the horizontal distance the ball will travel, we can use the horizontal velocity and the time of flight. The time of flight can be determined using the vertical motion equation:
h = (1/2)gt^2
Where h is the initial vertical displacement (1.7 m), g is the acceleration due to gravity (9.8 m/s^2), and t is the time of flight.
Rearranging the equation to solve for t:
t = sqrt(2h / g)
Substituting the given values:
t = sqrt(2 * 1.7 / 9.8) = 0.57 s (rounded to two decimal places)
Now that we have the time of flight, we can calculate the horizontal distance using the formula:
d = v * t
Where d is the distance, v is the horizontal velocity (8 m/s), and t is the time of flight.
Substituting the given values:
d = 8 * 0.57 = 4.56 m
Therefore, the ball will land approximately 4.56 meters away from the gun.