Final answer:
The object's speed is approximately 1.05 m/s, and its mass is approximately 42.9 kg. These values were calculated using the known kinetic energy and momentum, along with the formulas for kinetic energy and momentum.
Step-by-step explanation:
To find the speed and mass of the object given its kinetic energy and momentum, we use the following equations:
- Kinetic Energy (KE) = (1/2)mv²
- Momentum (p) = mv
Where m is the mass, v is the velocity, and p is the momentum.
We can rearrange the momentum equation to find the velocity as:
v = p / m
Using the kinetic energy equation, we can then express the mass in terms of kinetic energy and velocity:
m = (2 * KE) / v²
So, to calculate the speed (v), we need to know the mass. However, since we are not given the mass directly, we must use the two equations together.
First, we need to solve for the mass using both the kinetic energy and momentum:
KE = (1/2) * (p / v) * v² => p² = 2 * KE * v
Isolating v, we get:
v = p / sqrt(2 * KE)
Substituting the given values, KE = 920 J and p = 45.0 kg.m/s:
v = 45.0 kg.m/s / sqrt(2 * 920 J) => v = 45.0 kg.m/s / sqrt(1840 kg².m²/s²)
v = 45.0 kg.m/s / 42.9 m/s
v ≈ 1.05 m/s
Next, we use this velocity to find the mass:
m = p / v => m = 45.0 kg.m/s / 1.05 m/s
m ≈ 42.9 kg
So the speed of the object is approximately 1.05 m/s, and the mass is approximately 42.9 kg.