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Chapter 4: Q. 6 (page 105)

6. A rocket-powered hockey puck moves on a horizontal frictionless table. FIGURE EX4.6 shows graphs of vxand vy, the x - and y-components of the puck's velocity. The puck starts at the origin.

a. In which direction is the puck moving at ? Give your answer as an angle from the x-axis.

b. How far from the origin is the puck at ?

Short Answer

Expert verified

Part (a) The angle from the x-axis is 62°

Part (b) The distance from the origin is180cm

Step by step solution

01

Part (a)  

At t=2sthe graphs give vx=16cm/sand vy=30cm/s. The angle made by the vector v→with the x-axis can thus be found as

θ=tan−1vyvx=tan−130cm/s16cm/s=62°

above the x-axis

02

Part (b)

Aftert=5s , the puck has traveled a distance given by:

The displacement in x-direction

role="math" localid="1647460935572" x1=x0+∫05svxdt=0m+areaundervx−tcurve=12(40cm/s)(5s)=100cm

The displacement in y-direction

y1=y0+∫05svydt=0m+areaundervy−tcurve=(30cm/s)(5s)=150cm

The distance from the origin is

r1=x12+y12=(100cm)2+(150cm)2=180cm

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