## Math Problem Statement

A father demonstrates projectile motion to his children by placing a pea on his fork's handle and rapidly depressing the curved tines, launching the pea to heights above the dining room table. Suppose the pea is launched at 7.31 m/s at an angle of 69.0° above the table. With what speed (in m/s) does the pea strike the ceiling 1.90 m above the table?

HINT

Use the kinematic equations to find the *x*- and *y*-components of the pea's velocity when it hits the ceiling. Then use the Pythagorean theorem to find the speed.

*Click the hint button again to remove this hint.*

m/s

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Projectile Motion

Kinematics

Trigonometry

### Formulas

v_x = v_0 * cos(θ)

v_y = v_0 * sin(θ)

v_y^2 = v_{0y}^2 - 2g * (y_f - y_0)

v = √(v_x^2 + v_y^2)

### Theorems

Pythagorean Theorem

Kinematic Equations of Motion

### Suitable Grade Level

Grades 10-12

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