Question

Мяч брошен вертикально вверх с начальной скоростью 20 м/с.Найти скорость мяча на высоте 10м?

Answer 1

S=(v1^2-v0^2)/2a
10=(v1^2-400)/-20
(v1^2-400)=-200
v1^2=200
v1=10sqrt2

Answer 2

Problem Analysis

We are given that a ball is thrown vertically upwards with an initial velocity of 20 m/s. We need to find the velocity of the ball when it reaches a height of 10 m.

Solution

To solve this problem, we can use the equations of motion for vertical motion under constant acceleration. The acceleration due to gravity is constant and equal to 9.8 m/s^2.

Let's break down the problem into steps:

Step 1: Find the time taken for the ball to reach a height of 10 m. - We can use the equation: y = y0 + v0t - (1/2)gt^2, where: - y is the final height (10 m), - y0 is the initial height (0 m), - v0 is the initial velocity (20 m/s), - g is the acceleration due to gravity (-9.8 m/s^2), - t is the time taken.

Using the equation, we can rearrange it to solve for t: 10 = 0 + 20t - (1/2)(9.8)t^2

Step 2: Solve the quadratic equation to find the time taken. - Rearranging the equation, we get: 4.9t^2 - 20t + 10 = 0 - We can solve this quadratic equation using the quadratic formula: t = (-b ± √(b^2 - 4ac)) / (2a) - a = 4.9, b = -20, c = 10

Step 3: Calculate the velocity of the ball at a height of 10 m. - Once we have the time taken, we can use the equation: v = v0 - gt, where: - v is the final velocity, - v0 is the initial velocity (20 m/s), - g is the acceleration due to gravity (-9.8 m/s^2), - t is the time taken.

Now, let's calculate the time taken and the velocity of the ball at a height of 10 m.

Calculation

Step 1: Find the time taken for the ball to reach a height of 10 m. Using the equation 10 = 0 + 20t - (1/2)(9.8)t^2, we can solve for t.

Step 2: Solve the quadratic equation to find the time taken. Using the quadratic formula, we have: t = (-(-20) ± √((-20)^2 - 4(4.9)(10))) / (2(4.9))

Simplifying the equation, we get: t = (20 ± √(400 - 196)) / 9.8

Calculating the values inside the square root, we get: t = (20 ± √(204)) / 9.8

Taking the square root of 204, we get: t = (20 ± 14.28) / 9.8

Simplifying further, we have two possible values for t: - t1 = (20 + 14.28) / 9.8 ≈ 3.43 seconds - t2 = (20 - 14.28) / 9.8 ≈ 0.57 seconds

Since the ball is thrown upwards, we consider the positive value of time, t1 = 3.43 seconds.

Step 3: Calculate the velocity of the ball at a height of 10 m. Using the equation v = v0 - gt, we can calculate the velocity.

Substituting the values, we have: v = 20 - (9.8)(3.43)

Calculating the value, we get: v ≈ -13.34 m/s

Answer

The velocity of the ball at a height of 10 m is approximately -13.34 m/s.