A ball is thrown straight up from a bridge at a speed of 11.0 m/s. What will be its velocity (speed and direction) after 2.0 seconds?
V = Vo + g*t = 11 + (-9.8)*2 = -8.6 m/s,
The negative sign means the ball is falling.
To find the velocity of the ball after 2.0 seconds, we need to consider the acceleration due to gravity.
Since the ball is thrown straight up, the initial velocity is positive and the final velocity will be negative when the ball reaches its maximum height and starts falling back down.
We can use the equation for the velocity of an object in free fall:
v = u + gt
where:
v = final velocity
u = initial velocity
g = acceleration due to gravity (approximately 9.8 m/s²)
t = time
Given:
u = 11.0 m/s (positive because it is thrown upwards)
t = 2.0 seconds
g = 9.8 m/s²
Let's substitute the values into the equation:
v = 11.0 m/s + (9.8 m/s²)(2.0 s)
v = 11.0 m/s + 19.6 m/s
v ≈ 30.6 m/s
The velocity after 2.0 seconds will be approximately 30.6 m/s, in the opposite direction of the initial velocity.
To find the velocity of the ball after 2.0 seconds, we need to consider two things:
1. The initial velocity of the ball when it was thrown up.
2. The effect of gravity on the ball's velocity.
Let's break down the steps to calculate the velocity:
Step 1: Determine the initial velocity.
The problem states that the ball was thrown up with a speed of 11.0 m/s. Since the ball was thrown straight up, the initial velocity is positive (+11.0 m/s) since it is moving in the positive direction.
Step 2: Determine the effect of gravity.
Gravity acts in the downward direction and causes the ball to slow down as it moves upward and accelerate as it moves downward. The acceleration due to gravity, denoted as "g," is approximately 9.8 m/s². Since the velocity decreases by 9.8 m/s for each second, the velocity at any given time can be calculated using the formula:
velocity = initial velocity + (acceleration due to gravity) × (time)
Step 3: Calculate the velocity after 2.0 seconds.
Using the formula mentioned above, we can plug in the values:
velocity = 11.0 m/s + (-9.8 m/s²) × (2.0 s)
Simplifying the equation:
velocity = 11.0 m/s - 19.6 m/s
velocity = -8.6 m/s
The velocity after 2.0 seconds will be -8.6 m/s. The negative sign indicates that the ball is moving downward (opposite to the initial direction) with a speed of 8.6 m/s.