Recit%20Ch%203(1) - PHY2053 RECITATIONS, SPRING 2011...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
PHY2053 RECITATIONS, SPRING 2011 Recitation 3 (Chapter 3) Jan. 31-Feb. 4 Ch. 3 # 2. A jetliner is moving at a speed of 245 m/s. The vertical component of the plane’s velocity is 40.6 m/s. Determine the magnitude of the horizontal component of the plane’s velocity. REASONING AND SOLUTION The horizontal and vertical components of the plane's velocity are related to the speed of the plane by the Pythagorean theorem: 2 2 2 h v v v v = + . Solving for v h we have v v v h v 2 2 2 (245 m / s) 40.6 m / s) 242 m / s = - = - = 2 ( Ch. 3 # 8. In a mall, a shopper rides up an escalator between floors. At the top of the escalator, the shopper turns right and walks 9.00 m to a store. The magnitude of the shopper’s displacement from the bottom of the escalator to the store is 16.0 m. The vertical distance between the floors is 6.00 m. At what angle is the escalator inclined above the horizontal? REASONING Consider first the shopper’s ride up the escalator. Let the diagonal length of the escalator be L , the height of the upper floor be H , and the angle that the escalator makes with respect to the horizontal be θ (see the diagram). Because L is the hypotenuse of the right triangle and H is opposite the angle θ , the three quantities are related by the inverse sine function: 1 1 o sin sin h H h L θ - - = = (1.4) Now consider the entire trip from the bottom to the top of the escalator (a distance L ), and then from the top of the escalator to the store entrance (a distance s ). The right turn between these two parts of the trip means that they are perpendicular (see the diagram). The shopper’s total displacement has a magnitude D , and this serves as the hypotenuse of a right triangle with L and s . From the Pythagorean theorem, the three sides are related as follows: 2 2 2 D L s = + . SOLUTION Solving 2 2 2 D L s = + for the length L of the escalator gives 2 2 L D s = - . We now use this result and the relation 1 sin H L - = to obtain the angle θ : ( 29 ( 29 1 1 1 2 2 2 2 6.00 m sin sin sin 27.0 16.0 m 9.00 m H H L D s - - - = = = = - - o 1 s Entire view Up the escalator
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Ch. 3 # 16. A skateboarder shoots off a ramp with a velocity of 6.6 m/s, directed at an angle of 58° above the horizontal. The end of the ramp is 1.2 m above the ground. Let the x axis be parallel to the ground, the + y direction be vertically upward, and take as the origin the point on the ground
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/21/2011 for the course PHY 1500 taught by Professor Staff during the Spring '09 term at University of Central Florida.

Page1 / 6

Recit%20Ch%203(1) - PHY2053 RECITATIONS, SPRING 2011...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online