A sled is moving at a constant speed down a surface inclined at 45.0° with the horizontal and travels 30 meters in 4 seconds. Calculate the vertical velocity of the sled at the end of 4 seconds.
To calculate the vertical velocity of the sled at the end of 4 seconds, we need to break down the sled's motion into its horizontal and vertical components.
First, let's calculate the horizontal velocity (Vx) of the sled. We know that the sled is moving at a constant speed, so the horizontal velocity is the same throughout its motion.
We can use the formula for horizontal velocity:
Vx = d / t
where Vx is the horizontal velocity, d is the horizontal distance traveled, and t is the time taken.
In this case, the horizontal distance traveled (d) is 30 meters, and the time taken (t) is 4 seconds.
Substituting the values into the formula, we get:
Vx = 30 m / 4 s
Now, let's calculate the vertical velocity (Vy) of the sled. The vertical velocity changes due to the effect of gravity, which acts vertically downward.
We can use the formula for vertical velocity:
Vy = V0 * sin(θ) - g * t
where Vy is the vertical velocity, V0 is the initial vertical velocity (which we assume to be zero in this case), θ is the angle of inclination with the horizontal (45° in this case), g is the acceleration due to gravity (9.8 m/s²), and t is the time taken.
Substituting the values into the formula, we get:
Vy = 0 * sin(45°) - 9.8 m/s² * 4 s
Simplifying the equation, we get:
Vy = -9.8 m/s² * 4 s
Vy = -39.2 m/s
The negative sign indicates that the sled is moving downward vertically. Therefore, the vertical velocity of the sled at the end of 4 seconds is -39.2 m/s.
speed=distance/time=7.5m/s
at the end, vertical veloicty=7.5 cos45