Answered

A rock is projected with a total initial velocity of 35 m/s and a vertical component of 23 m/s. Find the total flight time and range of the rock.



Answer :

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.

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