Final answer:
The initial speed of the bullet, calculated using kinematic equations and considering the acceleration due to gravity and the ascent time of 5 seconds, is 49 m/s.
Step-by-step explanation:
To ascertain the initial speed of a bullet shot straight up that returns to its starting point in 10 seconds, we rely on kinematic equations for uniformly accelerated motion, with the acceleration being due to gravity (g = 9.8 m/s2). The time it takes for the bullet to ascend and descend is equal, so we can say that the ascent time is 5 seconds. Using the equation v = u + at, where v is the final velocity (0 m/s at the peak), u is the initial velocity, a is the acceleration due to gravity (-9.8 m/s2 because it's acting against the bullet going upwards), and t is the time (5 seconds for the ascent), we can solve for u.
Setting the equation for the ascent phase, we have: 0 = u - (9.8 m/s2) (5 s). Solving for u, we find that the initial velocity of the bullet is 49 m/s.