An object with mass 110 kg moved in outer space. When it was at location < 11, -35, -7 > its speed was 17.5 m/s. A single constant force < 230, 420, -230 > N acted on the object while the object moved to location < 16, -41, -13 > m. What is the speed of the object at this final location?
To find the speed of the object at the final location, we need to calculate the change in velocity of the object. The change in velocity can be calculated using the formula:
Δv = F/m
Where:
Δv is the change in velocity
F is the force acting on the object
m is the mass of the object
Since the force acting on the object is constant, we can calculate the change in velocity by dividing the force by the mass of the object.
Given:
Mass of the object (m) = 110 kg
Force acting on the object (F) = < 230, 420, -230 > N
To find the change in velocity, we need to divide the force by the mass:
Δv = F/m = < 230, 420, -230 > N / 110 kg
Doing the calculations:
Δv = < 2.09, 3.82, -2.09 > m/s^2
Now, we need to find the final velocity of the object using the initial velocity and the change in velocity. The final velocity can be calculated using the equation:
v_f = v_i + Δv
Where:
v_f is the final velocity
v_i is the initial velocity
Δv is the change in velocity
Given:
Initial velocity (v_i) = 17.5 m/s
Change in velocity (Δv) = < 2.09, 3.82, -2.09 > m/s^2
To find the final velocity, we need to add the initial velocity and the change in velocity:
v_f = v_i + Δv = 17.5 m/s + < 2.09, 3.82, -2.09 > m/s^2
Doing the calculations:
v_f = < 19.59, 21.32, 15.41 > m/s
Therefore, the speed of the object at the final location is the magnitude of the final velocity:
Speed = ||v_f|| = sqrt((19.59)^2 + (21.32)^2 + (15.41)^2) m/s
Doing the calculations:
Speed = 30.9 m/s
So, the speed of the object at the final location is 30.9 m/s.