Solve 2D Motion Problem: Initial Velocity 8.40m/s, Angle 17°

In summary, a ball is thrown from an upper-story window of a building with an initial velocity of 8.40m/s at an angle of 17° below the horizontal. It takes 4.00 seconds for the ball to strike the ground. We are asked to find the horizontal distance from the base of the building where the ball strikes, the height from which the ball was thrown, and the time it takes for the ball to reach a point 10.0 m below the launching level. We can use trigonometric functions to solve for these values.
  • #1
chocolatelover
239
0

Homework Statement


A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of 8.40m/s at an angle of 17° below the horizontal. It stikes the ground 4.00 s later.

a. How far horizontally from the base of the building does the ball strike the ground?
b. Find the height from which the ball was thrown
c. How long does it take the ball to reach a point 10.0 m below the level of launching?

Homework Equations





The Attempt at a Solution



I don't understand how it can be 17° below the horizonal axis. If it is below the x axis, doesn't that mean that it is negative? Would I just use cos and sin for parts a and b? Could someone please give me a hint on part c?

Thank you very much
 
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  • #2
It's not impossible to throw a ball downwards from a building. You have a velocity, time, and you have the angle to the horizontal. Remember, break projectile motion problems into x and y situations.
 
  • #3
Thank you very much

Regards
 

1. What is the formula for solving 2D motion problems with given initial velocity and angle?

The formula for solving 2D motion problems with given initial velocity and angle is:
Vx = V0 * cos(θ)
Vy = V0 * sin(θ) - gt
Where Vx and Vy are the horizontal and vertical components of the velocity, V0 is the initial velocity, θ is the angle, and g is the acceleration due to gravity (9.8 m/s²).

2. How do you find the maximum height and range in a 2D motion problem with given initial velocity and angle?

To find the maximum height and range, we can use the following formulas:
Maximum height (H) = (V0 * sin(θ))^2 / (2 * g)
Range (R) = (V0^2 * sin(2θ)) / g
Where V0 is the initial velocity, θ is the angle, and g is the acceleration due to gravity (9.8 m/s²).

3. Can you solve a 2D motion problem with only the initial velocity and angle given?

Yes, a 2D motion problem can be solved with only the initial velocity and angle given. However, it is important to note that the initial velocity must be broken down into its horizontal and vertical components (Vx and Vy) using the formula Vx = V0 * cos(θ) and Vy = V0 * sin(θ) - gt before solving the problem.

4. What is the importance of understanding 2D motion problems in physics?

Understanding 2D motion problems in physics is important because it helps us analyze and predict the motion of objects in two dimensions. This is applicable in many real-life situations, such as predicting the trajectory of a projectile or the motion of a car on a curved road. It also helps us understand the fundamental principles of motion, such as velocity, acceleration, and displacement.

5. Are there any limitations to solving 2D motion problems with the given initial velocity and angle?

Yes, there are some limitations to solving 2D motion problems with only the initial velocity and angle given. These limitations include neglecting air resistance, assuming a constant acceleration due to gravity, and assuming a flat surface with no friction. In real-life scenarios, these factors may affect the motion of the object and may need to be taken into consideration for a more accurate solution.

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