Question

Игрок в гольф ударил мяч так, что угол вылета оказался равен 45°, а максимальная высота подъема составила 1,5 м. а) Определите начальную скорость, с которой ударили по мячу.б) Рассчитайте время подъема мяча.в) Вычислите дальность полета мяча.​

Answer 1

А)16 км Б)2,3 км В)43 км

Answer 2

Golf Ball Trajectory Calculation

To determine the initial velocity, time of ascent, and distance traveled by the golf ball, we can use the following equations of projectile motion:

1. Initial Velocity (v0): The initial velocity of the golf ball can be calculated using the equation:

v0 = (R / cosθ) × √(g / 2h)

Where: - v0 is the initial velocity - R is the range (distance traveled by the ball) - θ is the launch angle (45° in this case) - g is the acceleration due to gravity (approximately 9.8 m/s²) - h is the maximum height reached by the ball (1.5 m)

Plugging in the given values, we can calculate the initial velocity.

2. Time of Ascent (t): The time taken by the ball to reach its maximum height can be calculated using the equation:

t = √(2h / g)

Plugging in the given value of the maximum height, we can calculate the time of ascent.

3. Distance Traveled (R): The distance traveled by the ball can be calculated using the equation:

R = (v0² × sin2θ) / g

Plugging in the calculated value of the initial velocity and the given launch angle, we can calculate the distance traveled.

Let's calculate each of these values step by step.

a) Calculating the Initial Velocity (v0): Using the equation mentioned above, we can calculate the initial velocity:

v0 = (R / cosθ) × √(g / 2h)

Given: - θ = 45° - h = 1.5 m

We need to calculate R to find the initial velocity. Unfortunately, the range (R) is not provided in the question. Could you please provide the range (distance traveled by the ball) as well?

b) Calculating the Time of Ascent (t): Using the equation mentioned above, we can calculate the time of ascent:

t = √(2h / g)

Given: - h = 1.5 m

Plugging in the given value, we can calculate the time of ascent.

c) Calculating the Distance Traveled (R): Using the equation mentioned above, we can calculate the distance traveled:

R = (v0² × sin2θ) / g

Given: - θ = 45°

We need to calculate the initial velocity (v0) to find the distance traveled. Unfortunately, the initial velocity is not provided in the question. Could you please provide the initial velocity as well?

Once we have the missing values (initial velocity and range), we can calculate the time of ascent and the distance traveled by the golf ball.