a toy car runs off the edge of a table that is 1.225 m high. if the car lands .400 m from the base of the table (A) how long does it take for the car to fall and (B) what is the horizontal velocity of the car?
0.5 seconds
0.499
To find the time it takes for the car to fall, we can use the equation for free fall:
y = (1/2)gt^2
Where:
y = vertical displacement
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
(A) Solving for time:
Given that the car falls from a height of 1.225 m and assuming it falls vertically:
1.225 m = (1/2)(9.8 m/s^2)(t^2)
Rearranging the equation and solving for t:
t^2 = (2 * 1.225 m) / 9.8 m/s^2
t^2 = 0.25 s^2
Taking the square root of both sides:
t = √(0.25 s^2)
t = 0.5 s
Therefore, it takes the car 0.5 seconds to fall.
(B) To find the horizontal velocity of the car, we can use the equation:
v = d / t
Where:
v = velocity
d = horizontal displacement
t = time
Given that the car lands 0.400 m from the base of the table and the time of fall is 0.5 s:
v = 0.400 m / 0.5 s
v = 0.8 m/s
Therefore, the horizontal velocity of the car is 0.8 m/s.
To find the time it takes for the toy car to fall, we can use the equation for vertical motion:
\(h = \frac{1}{2}gt^2\),
where:
- \(h\) is the height of the table, which is 1.225 m,
- \(g\) is the acceleration due to gravity, which is approximately 9.81 m/s², and
- \(t\) is the time taken to fall.
To solve for \(t\), we rearrange the equation:
\(t = \sqrt{\frac{2h}{g}}\).
Substituting the values given,
\(t = \sqrt{\frac{2(1.225)}{9.81}} \approx \sqrt{0.2499} \approx 0.4999\) seconds.
Therefore, the toy car takes approximately 0.4999 seconds to fall.
To find the horizontal velocity of the car, we can use the equation for horizontal motion:
\(d = vt\),
where:
- \(d\) is the horizontal distance traveled by the car, which is 0.400 m,
- \(v\) is the horizontal velocity of the car, and
- \(t\) is the time taken to fall, which we calculated as approximately 0.4999 seconds.
Rearranging the equation to solve for \(v\),
\(v = \frac{d}{t}\),
\(v = \frac{0.400}{0.4999} \approx 0.8002\) m/s.
Therefore, the horizontal velocity of the toy car is approximately 0.8002 m/s.