Question

Теннисный мяч подан с высотой 2 м 10 см и пролетел над самой сеткой,высота которой 90 см.На каком расстоянии от сетки мяч ударится о землю,если он подан от черты,находящейся от сетки на расстоянии 12 м и летит практически прямолинейно?

Answer 1

1) (210-90):12=10(см)-разница в снижении мяча каждый метр
2) 90:10=9(м)-расстояние от сетки до места,где ударится мяч о землю

Answer 2

Calculation of the Distance from the Net to where the Tennis Ball Hits the Ground

To calculate the distance from the net to where the tennis ball hits the ground, we can use the given information about the height from which the ball was served and the height of the net.

Given: - Height from which the ball was served: 2 meters 10 centimeters - Height of the net: 90 centimeters - Distance from the net: 12 meters

To solve this problem, we can use the concept of projectile motion. When a tennis ball is served, it follows a parabolic trajectory. The vertical motion of the ball can be analyzed separately from the horizontal motion.

First, let's calculate the time it takes for the ball to reach its maximum height. We can use the equation:

time = (final velocity - initial velocity) / acceleration

In this case, the initial velocity is the velocity at which the ball is served, and the final velocity is zero at the maximum height. The acceleration is due to gravity and is approximately 9.8 m/s^2.

Using the given height from which the ball was served (2 meters 10 centimeters), we can convert it to meters and calculate the initial velocity:

initial velocity = sqrt(2 * acceleration * height)

Next, we can calculate the time it takes for the ball to reach its maximum height:

time = initial velocity / acceleration

Now, let's calculate the time it takes for the ball to hit the ground after reaching its maximum height. The total time of flight can be calculated as twice the time it takes to reach the maximum height:

total time of flight = 2 * time

Finally, we can calculate the horizontal distance traveled by the ball using the formula:

horizontal distance = total time of flight * horizontal velocity

Since the ball is traveling in a straight line, the horizontal velocity remains constant throughout the flight. We can calculate the horizontal velocity using the given distance from the net (12 meters) and the total time of flight:

horizontal velocity = distance from the net / total time of flight

Now, we can substitute the values into the formulas and calculate the distance from the net to where the ball hits the ground.

Calculation:

1. Convert the given heights to meters: - Height from which the ball was served: 2.10 meters - Height of the net: 0.90 meters

2. Calculate the initial velocity: - initial velocity = sqrt(2 * 9.8 * 2.10) = 6.06 m/s

3. Calculate the time it takes to reach the maximum height: - time = 6.06 / 9.8 = 0.62 seconds

4. Calculate the total time of flight: - total time of flight = 2 * 0.62 = 1.24 seconds

5. Calculate the horizontal velocity: - horizontal velocity = 12 / 1.24 = 9.68 m/s

6. Calculate the horizontal distance traveled by the ball: - horizontal distance = 9.68 * 1.24 = 12 meters

Therefore, the tennis ball will hit the ground at a distance of 12 meters from the net.

Please note that this calculation assumes ideal conditions and neglects factors such as air resistance and spin on the ball, which can affect the actual trajectory of the ball.