Hot air balloon A is rising upward a rate of 5.0 m/s. A passenger aboard balloon A observes balloon B rising upward at a relative rate of 7.5 m/s. What is the velocity of balloon B relative to the ground? Assume that up is positive.
huh?
5 + 7.5
12.5
To determine the velocity of balloon B relative to the ground, we need to calculate the difference between the velocity of balloon B observed by the passenger on balloon A and the velocity of balloon A.
Given:
Velocity of balloon A (v_A) = 5.0 m/s (upward)
Relative rate of balloon B observed by passenger on balloon A (v_A-B) = 7.5 m/s (upward)
To find the velocity of balloon B relative to the ground (v_B), we apply the concept of relative velocities:
v_B = v_A + v_A-B
Substituting the given values:
v_B = 5.0 m/s + 7.5 m/s
v_B = 12.5 m/s
Therefore, the velocity of balloon B relative to the ground is 12.5 m/s (upward).
To find the velocity of balloon B relative to the ground, we need to find the vector sum of the velocity of balloon B relative to balloon A and the velocity of balloon A relative to the ground.
Given:
Velocity of balloon A relative to the ground = +5.0 m/s (upward)
Relative rate of balloon B with respect to balloon A = +7.5 m/s (upward)
We can assume that the positive direction is upward, so we take both velocities as positive.
To find the velocity of balloon B relative to the ground (v_Bg), we add the two velocities:
v_Bg = v_Ba + v_Ag,
where v_Ba is the velocity of balloon B relative to balloon A and v_Ag is the velocity of balloon A relative to the ground.
v_Bg = +7.5 m/s + (+5.0 m/s)
Adding these two velocities together, we get:
v_Bg = +12.5 m/s
Therefore, the velocity of balloon B relative to the ground is +12.5 m/s (upward).