## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 2 - Acute Angles and Right Triangles - Section 2.3 Finding Trigonometric Function Values Using a Calculator - 2.3 Exercises - Page 70: 88

#### Answer

The car is traveling at a speed of 77.8 mph when it hits the truck.

#### Work Step by Step

$V_1 = 90~mph$ We can convert $90~mph$ to units of feet/s: $V_1 = 90~mph\times \frac{1~hr}{3600~s}\times \frac{5280~ft}{1~mile} = 132~ft/s$ $D = \frac{1.05~(V_1^2-V_2^2)}{64.4~(K_1+K_2+sin~\theta)}$ $D~[64.4~(K_1+K_2+sin~\theta)] = 1.05~(V_1^2-V_2^2)$ $V_2^2 = V_1^2-\frac{D~[64.4~(K_1+K_2+sin~\theta)]}{1.05}$ $V_2 = \sqrt{V_1^2-\frac{D~[64.4~(K_1+K_2+sin~\theta)]}{1.05}}$ $V_2 = \sqrt{(132~ft/s)^2-\frac{(200~ft)~[64.4~(0.4+0.02+sin~(-3.5^{\circ})]}{1.05}}$ $V_2 = 114.1~ft/s$ We can convert $114.1~ft/s$ to units of mph: $V_2 = 114.1~ft/s \times \frac{3600~s}{1~hr}\times \frac{1~mile}{5280~ft} = 77.8~mph$ The car is traveling at a speed of 77.8 mph when it hits the truck.

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