Q1-a stone is thrown upwards into the what is the magnitude and direction of its acceleration ?
Q2-if a ball is thrown horizontally from a top of a cliff and takes 3 seconds to reach the beach below. Calculate the height if the cliff by considering the vertical motion only
Q1. a = g = -9.8 m/s^2 = 9.8 m/s^2 Downward.
Q2. h = 0.5g*t^2 = 4.9*3^2 = 44.1 m.
Q1: To determine the magnitude and direction of acceleration for a stone thrown upwards, we need to understand the forces acting on the stone.
When the stone is thrown upwards, the primary force acting on it is the force of gravity. However, since the stone is moving against the direction of gravity, the acceleration due to gravity (-9.8 m/s²) will oppose the stone's motion.
Therefore, the magnitude of the stone's acceleration is 9.8 m/s² (ignoring air resistance), and its direction is downwards.
Q2: To calculate the height of the cliff using only the vertical motion of a ball thrown horizontally, we can utilize the equations of motion.
Since the horizontal velocity of the ball is constant throughout its motion, it does not affect the vertical motion. We can focus solely on the vertical component of its motion.
The equation that relates the vertical displacement (height), initial vertical velocity, time, and acceleration is:
h = (1/2) * a * t²
In this case, we know that the time it takes for the ball to reach the beach below is 3 seconds. The acceleration due to gravity, a, is -9.8 m/s² (negative because it opposes the motion in the vertical direction).
h = (1/2) * (-9.8 m/s²) * (3 s)²
h = (-4.9 m/s²) * 9 s²
h = -44.1 m²/s²
Since height cannot be negative, we take the absolute value of the result:
height = |h| = 44.1 meters
Therefore, the height of the cliff is approximately 44.1 meters.