1) It takes 2.86 seconds
To determine the time of flight, we need to evaluate the stone's vertical motion, characterized by uniformly accelerating motion (free fall) where gravitational acceleration is constant.
The vertical position at time t is expressed as
In this case, we define downward as the positive direction
as the initial vertical velocity (which is zero, given the projectile is launched horizontally)
t signifies the elapsed time
g indicates gravitational acceleration
In this scenario, we have
s = 40 m (vertical distance corresponds to the height of the tower)
By solving for t, we can determine the time of the projectile's flight:
Thus, the projectile takes 2.86 s to reach the ground.
2) Horizontal distance: 57.2 m
The projectile's horizontal motion is uniform; in fact, no forces affect it along that direction, rendering the horizontal acceleration zero, therefore, the horizontal velocity remains constant.
The initial horizontal velocity of the projectile is
Consequently, to compute the horizontal distance traveled by the projectile, we can utilize the formula
And by substituting the time of flight, we find out when the projectile impacts the ground:
t = 2.86 s
Thus, we derive:
The answer is:
Details are as follows:
According to the problem, we have
The combined mass of A and B is 60kg
A's speed is 2m/s
B's speed is 1m/s
The mass of the bag is 5kg
Typically, the momentum of astronaut A along with the bag is defined by
To prevent a collision, astronaut A should maintain a speed that is either equal to or less than astronaut B's speed
Thus, the minimum speed astronaut A should achieve corresponds to that of astronaut B, which is 1
Consequently,