
Figure 1
Two identical spheres are released from a device at time from the same height
, as shown above. The device is shown in Figure 1.
Sphere A has no initial velocity and falls straight down. Sphere B is given an initial horizontal velocity of magnitude and travels a horizontal distance
before it reaches the ground. The spheres reach the ground at the same time
, even though Sphere B has more distance to cover before landing. Air resistance is negligible.
The dots in Figure 2 represent Spheres A and B. Draw a free-body diagram showing and labeling the forces (not components) exerted on each sphere at time .

Figure 2
Derive an expression for the total time of flight of each sphere, in terms of and physical constants as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference book.
On the axes in Figure 3, sketch and label a graph of the horizontal component of the velocity of Sphere A and of Sphere B as a function of time.

Figure 3
Justify whether your answers to part b) and part c) support the finding that the spheres reach the ground at the same time, even though they travel different distances.
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