Math Problem Statement

You must include a picture for this question, variable lists, and all appropriate formulas and work for full credit.

Mrs. Hickman is walking into the building on a snowy day. On her way she sees Mr. Lewis 4.50 meters away. Angry that she didn’t get a snow day, Mrs. Hickman fires a snowball horizontally at a speed of 8.00 m/s from a height of 1.75 m. Upon seeing Mrs. Hickman wind up, Mr. Lewis begins sprinting towards Mrs. Hickman with an acceleration of 1 m/s^2 (from rest). How long will the snow ball be in the air before it hits Mr. Lewis? At what height above the ground will the snow ball hit Mr. Lewis? How far forward will Mr. Lewis accelerate before the snowball hits him?

Solution

Here is the diagram illustrating the snowball's trajectory and Mr. Lewis’s motion. Let me know if further clarification or additional details are needed!

Related Questions:

  1. What would happen if the snowball were thrown with an upward angle instead of horizontally?
  2. How would increasing Mr. Lewis’s acceleration to 2 m/s² change the outcome?
  3. What if Mrs. Hickman threw the snowball from a different height, say 3 meters?
  4. How would air resistance affect the snowball's trajectory?
  5. Can we calculate Mr. Lewis’s speed at the moment the snowball hits the ground?

Tip:

In problems involving projectile motion, always break the motion into horizontal and vertical components for easier analysis.

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Math Problem Analysis

Mathematical Concepts

Projectile Motion
Kinematics
Vertical and Horizontal Components

Formulas

Vertical motion: s = ut + (1/2)gt^2
Horizontal motion: s = vt
Acceleration: s = ut + (1/2)at^2

Theorems

Equations of Motion

Suitable Grade Level

Grades 10-12

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