What is the maximum height achieved if a 0.800 kg mass is thrown straight upward with an initial speed of 40.0 m·s–1? Ignore the effect of air resistance.
V^2 = Vo^2 + 2g*h = 0 at max. ht.
40^2 - 19.6*h = 0
19.6h = 1600
h = 81.6 m.
To find the maximum height achieved by the mass, we can use the equation for projectile motion:
h = (v^2 - u^2) / (2g)
where:
h = maximum height
v = final velocity (0 m/s at the highest point)
u = initial velocity (40.0 m/s)
g = acceleration due to gravity (9.8 m/s^2)
Plugging in the known values into the equation:
h = (0^2 - 40.0^2) / (2 * 9.8)
Calculating:
h = (-1600) / 19.6
h ≈ -81.63 meters
Since the height cannot be negative, the maximum height achieved is approximately 81.63 meters.
To determine the maximum height achieved by the mass, we can use the concepts of kinematics and conservation of energy. Here is how to find the answer step by step:
Step 1: Identify the given values
- Mass (m): 0.800 kg
- Initial velocity (v₀): 40.0 m/s
- Acceleration due to gravity (g): 9.8 m/s²
Step 2: Determine the final velocity at the maximum height
When the mass reaches its maximum height, it momentarily comes to rest before falling back down. At this point, the final velocity (vf) is zero.
Step 3: Apply the kinematic equation
The kinematic equation that relates initial velocity, final velocity, acceleration, and displacement is:
vf² = v₀² + 2ad
Since vf is zero, this equation simplifies to:
v₀² = -2ad
Step 4: Find the acceleration
As the mass is thrown straight upward, the acceleration is in the opposite direction to gravity. Therefore, the acceleration is -g.
Step 5: Solve for the displacement (height)
Substituting the known values into the equation:
v₀² = -2(-g)d
Simplifying the equation:
d = v₀² / (2g)
Step 6: Calculate the maximum height
Inserting the given values into the equation:
d = (40.0 m/s)² / (2 * 9.8 m/s²)
Calculating:
d ≈ 816.33 m
Therefore, the maximum height achieved by the mass is approximately 816.33 meters.