Calculating Initial Velocity & Angle of a Moving Ball

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In summary, the motion of a ball in the air can be described by two functions, x(t) = 84 + 27t and y(t) = 88 + 46t - 490t^2, with a=84 cm, b=27 cm/s, c=88 cm, d=46 cm/s, and e=-490 cm/s/s. To find the magnitude of the initial velocity, take the square root of the sum of the squares of the velocities in the x and y directions at t=0. To determine the angle between the initial velocity and the horizontal, find the arctan of the y velocity divided by the x velocity at t=0. A hint for solving this problem is to
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borow039
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A ball is moving through the air as shown. Its horizontal position x and vertical position y can be described by two functions: x(t) = a + b*t and y(t) = c + d*t + e*t*t.
Here t represents time and

a= 84 cm, b=27 cm/s, c=88 cm, d=46 cm/s and e=-490 cm/s/s.

What is the magnitude of the initial velocity of the ball? and what is the angle between the initial velocity and the horizontal?

Could anyone provide a much needed hint to get going on this problem?
 
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  • #2
Find dx/dt and dy/dt. That will give you vx and vy. Put t = 0 to get vo = sqrt(vx^2 + vy^2)
 
  • #3
ok i got it thanks so much!
 

1. What is initial velocity?

Initial velocity is the speed and direction at which an object begins to move. It is typically denoted as "v0" or "u" in equations and is measured in meters per second (m/s).

2. How is initial velocity calculated?

The initial velocity of a moving ball can be calculated using the equation v0 = √(vf2 - 2ad), where vf is the final velocity, a is the acceleration, and d is the distance traveled. Alternatively, it can be calculated using the formula v0 = u + at, where u is the initial velocity, a is the acceleration, and t is the time.

3. What factors affect the initial velocity of a moving ball?

The initial velocity of a moving ball is affected by factors such as the force applied to it, the angle at which it is thrown, and air resistance. The mass and shape of the ball may also play a role in determining its initial velocity.

4. How is the angle of a moving ball calculated?

The angle of a moving ball can be calculated using the equation θ = tan-1(vy/vx), where θ is the angle, vy is the vertical component of the velocity, and vx is the horizontal component of the velocity.

5. What are some practical applications of calculating initial velocity and angle of a moving ball?

Calculating the initial velocity and angle of a moving ball is important in various fields such as sports, engineering, and physics. It can help in designing and optimizing equipment and techniques for throwing, launching, or hitting objects. It is also useful for predicting the trajectory and behavior of objects in motion, which can have practical applications in fields such as ballistics and flight dynamics.

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