an autographed baseball rolls off of a .70m high desk and strikes the floor .25m away from the base of the desk. How fast was it rolling?
To find the speed at which the autographed baseball was rolling when it struck the floor, we can use the principles of projectile motion and conservation of energy.
First, we need to determine the initial vertical velocity of the baseball as it falls from a height of 0.70m. We can do this by using the formula for vertical displacement in free fall:
Δy = v₀y * t + (1/2) * g * t²
Here, Δy is the vertical displacement (0.70m), v₀y is the initial vertical velocity, t is the time of flight, and g is the acceleration due to gravity (-9.8 m/s²). Since the baseball starts with an initial vertical velocity of 0 (assuming it is dropped vertically), the equation simplifies to:
0.70m = (1/2) * (-9.8 m/s²) * t²
Next, we solve for t. Rearranging the equation:
t² = (2 * 0.70m) / 9.8 m/s²
t² ≈ 0.1429s²
t ≈ √(0.1429s²)
t ≈ 0.3787s
Now, we will calculate the horizontal velocity of the baseball. The horizontal distance it travels, d, is given as 0.25m. The horizontal velocity, v₀x, can be found using the equation:
d = v₀x * t
Substituting the known values:
0.25m = v₀x * 0.3787s
Now, solve for v₀x:
v₀x = 0.25m / 0.3787s
v₀x ≈ 0.6606 m/s
Thus, the autographed baseball was rolling with an approximate speed of 0.6606 m/s when it struck the floor.
To find the speed at which the autographed baseball was rolling off the desk, we can use the equations of motion. The key information provided is the height the baseball fell from the desk (h = 0.70 m) and the horizontal distance it traveled (d = 0.25 m).
Let's assume the initial velocity of the baseball rolling off the desk is zero (u = 0) and the acceleration due to gravity is g = 9.8 m/s^2, acting vertically downwards.
Step 1: Find the time taken for the baseball to fall.
Using the equation of motion for vertical motion: h = (1/2)gt^2, where t represents the time
0.70 = (1/2)(9.8)t^2
0.70 = 4.9t^2
t^2 = 0.70 / 4.9
t^2 = 0.1429
t ≈ √0.1429
t ≈ 0.378 seconds
Step 2: Find the horizontal component of the velocity.
Using the equation of motion for horizontal motion: d = ut, where d represents the horizontal distance and u represents the initial horizontal velocity
0.25 = u × 0.378
u = 0.25 / 0.378
u ≈ 0.6616 m/s
Therefore, the speed at which the autographed baseball was rolling off the desk is approximately 0.6616 m/s.
Find out how long it takes to fall .7m
.7 = 4.9t^2
Now, with that t, and knowing that the horizontal velocity is constant,
.25 = vt
v = .25/t = .25/√(.7/4.9)