an arrow is shot from a cliff at an angle of 0 degrees with respect to the vertical at a speed of 30m/sec. It takes 4 seconds for the arrow to hit the ground. how high is the cliff?
To find the height of the cliff, we can use the kinematic equations of motion.
Step 1: Identify the known values:
- Initial velocity (Vi): 30 m/s (the speed at which the arrow is shot)
- Time (t): 4 seconds (the time it takes for the arrow to hit the ground)
- Angle (θ): 0 degrees with respect to the vertical (meaning the arrow is shot horizontally)
- Acceleration due to gravity (g): approximately 9.8 m/s^2 (assuming a constant value)
Step 2: Analyze the motion in the vertical direction:
Since the arrow is shot horizontally, the initial velocity in the vertical direction (Vy) is zero. The arrow experiences free fall motion with an acceleration of -g (negative because it acts in the opposite direction to the positive direction we defined).
Step 3: Calculate the height of the cliff:
Use the equation for displacement in the vertical direction:
Vy = Viy + at
Since Vy = 0, Viy = 0 (initial vertical velocity), and a = -g, we have:
0 = 0 + (-9.8) * 4
0 = -39.2
The displacement in the vertical direction (Δy) is equal to the height of the cliff. Thus, we have:
Δy = 0.5 * a * t^2
Δy = 0.5 * (-9.8) * (4^2)
Δy = 0.5 * (-9.8) * 16
Δy = -78.4
The negative sign indicates that the height is moving downward, so we take the absolute value to obtain the actual height:
Height of the cliff = |-78.4| = 78.4 meters
Therefore, the height of the cliff is 78.4 meters.