Math Problem Statement

Answer only no work needed

1. A projectile is launched with a velocity of 100 m/s at an angle of 30.0 degrees above the horizontal. What is its range? 2. A boy wants to throw a ball into his friend's window 20.0 m above the ground. Assuming it just reaches the window, he throws the ball at 55.0 degrees above the ground. At what velocity should he throw the ball? 3. A projectile is launched at 65.0 degrees. If it reaches its highest point in 8.0 seconds, at what initial velocity is it launched? 4. A football is kicked with an initial velocity of 30.0 m/s at an angle of 30.0 degrees above the horizontal. Determine the hang time of the ball. 5. A tiger attempts to leap onto a ledge at 7.75 m/s at an angle of 35 degrees above the horizontal. How far away from the ledge should the tiger jump in order to reach its maximum height?

Solution

  1. 884 m
  2. 23.8 m/s
  3. 97.3 m/s
  4. 3.06 s
  5. 2.88 m

Would you like further explanation for any of these answers or related details?

Here are 5 related questions to explore further:

  1. How does the angle of projection affect the range of a projectile?
  2. Why is the vertical component of velocity critical in reaching a specific height?
  3. How can time to the highest point help determine the initial velocity?
  4. What factors influence the hang time of a projectile?
  5. How does the horizontal distance to maximum height relate to the projectile's speed and angle?

Tip: Understanding the separation of horizontal and vertical motion in projectile problems simplifies solving them.

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Math Problem Analysis

Mathematical Concepts

Projectile motion
Kinematics
Trigonometry

Formulas

Range = (v^2 * sin(2θ)) / g
y = v * sin(θ) * t - 0.5 * g * t^2
v = g * t / sin(θ)
Hang time = 2 * v * sin(θ) / g
Horizontal distance = v * cos(θ) * time to max height

Theorems

Equations of motion
Trigonometric identities

Suitable Grade Level

Grades 10-12

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