1.A baseball pitcher stands 60' 6" from home plate. The ball the leaves the pitcher's hand from a height of 1.8 m through the strike zone at 65 m. If the batter has 0.4 seconds to react, how fast is the pitch travelling?
2.A rock is tossed slightly upward 10o at 1 m/s from a bridge 20 m above the water below. How far does the rock travel horizontally?
3.A soccer ball is rolled along a level table at 0.5 m/s and the table is 0.8 m off of the floor. How far will the ball travel beyond the table?
1. To find the speed of the pitch, we can use the formula: speed = distance / time.
- First, we need to convert the distance from feet and inches to meters. 60 feet 6 inches is approximately 18.44 meters.
- The ball travels through the strike zone at 65 meters. We can subtract the initial distance of the pitcher from this distance to find the distance the ball travels: 65 m - 18.44 m = 46.56 meters.
- The time the batter has to react is given as 0.4 seconds.
Now, we can calculate the pitch speed:
speed = distance / time = 46.56 m / 0.4 seconds = 116.4 m/s.
Therefore, the pitch is traveling at a speed of approximately 116.4 meters per second.
2. To find how far the rock travels horizontally, we can use the formula for horizontal distance traveled:
distance = initial velocity * time.
- The initial velocity is given as 1 m/s and the angle of projection is 10 degrees.
- We need to break down the initial velocity into its horizontal and vertical components.
- The horizontal component can be found by multiplying the initial velocity by the cosine of the angle: horizontal component = 1 m/s * cos(10o).
- The time of flight can be calculated using the formula for free-fall time: time = sqrt((2 * vertical distance) / acceleration due to gravity).
- The vertical distance is given as 20 meters and the acceleration due to gravity is approximately 9.8 m/s^2.
Now, we can calculate the horizontal distance:
distance = horizontal component * time = (1 m/s * cos(10o)) * time.
Therefore, we need to first calculate the time of flight and then multiply it by the horizontal component to find the horizontal distance traveled by the rock.
3. To find how far the soccer ball will travel beyond the table, we can use the formula for distance traveled:
distance = velocity * time.
- The velocity of the soccer ball is given as 0.5 m/s.
- The time can be calculated using the formula: time = height / velocity.
Now, we can calculate the distance beyond the table:
distance = velocity * time = 0.5 m/s * time.
Therefore, we need to first calculate the time of travel using the height of the table divided by the velocity of the soccer ball, and then multiply it by the velocity to find the distance traveled beyond the table.