Answer:
The flight time is 4.7 seconds and the range is 120 meters
Explanation:
The rock is a projectile in free fall. The motion can be modeled using kinematic equations, also known as SUVAT equations. We will use the below equation:
s = ut + ½ at²
where
- s is the displacement (distance and direction)
- u is the initial velocity (speed and direction)
- a is the acceleration
- t is the time
In the vertical direction, the displacement is s = 0 m, since the rock returns to ground level. The initial velocity is given to be u = 23 m/s. The acceleration of the rock is that due to gravity, a = -9.8 m/s². Plugging in and solving for time:
s = ut + ½ at²
0 = 23t + ½ (-9.8) t²
0 = 23t − 4.9t²
0 = 23 − 4.9t
t ≈ 4.69 s
The horizontal component of the initial velocity can be found with Pythagorean theorem.
c² = a² + b²
35² = 23² + b²
1225 = 529 + b²
b² = 696
b ≈ 26.4 m/s
In the horizontal direction, the acceleration of the rock is a = 0 m/s², assuming there is no air resistance. Given that the flight time is 4.69 seconds, the range of the rock is:
s = ut + ½ at²
s = (26.4) (4.69) + ½ (0) (4.69)²
s ≈ 124 m
Rounding the answers to two significant figures, the flight time is 4.7 seconds and the range is 120 meters.
