1. Lisa in her Lamborghini accelerates at the rate of ( 3.00i - 2.00 j) m/s^ 2,
ID: 1395215 • Letter: 1
Question
1. Lisa in her Lamborghini accelerates at the rate of ( 3.00i - 2.00 j) m/s^ 2, while Jill in her Jaguar accelerates at ( 1.00i + 3.00 j )m/s^ 2. They both start from rest at the origin of an xy coordinate system. After 5.00 s, (a) what is Lisa's speed with respect to Jill, (b) how far apart are they, and (c) what is Lisa's acceleration relative to Jill? 2. As some molten metal splashes, one droplet flies off to S the east with initial velocity vi at angle theta i above the horizontal, and another droplet flies off to the west with the same speed at the same angle above the horizontal as shown in Figure below. In terms of vi and theta i, find the distance between the two droplets as a function of time. 3. A pendulum with a cord of length r =1.00 m swings in a vertical plane (Fig. P4.70). When the pendulum is in the two horizontal positions 0=90.0 degree and theta=270 degree, its speed is 5.00m/s. Find the magnitude of (a) the radial g acceleration and (b) the tangential acceleration for these positions. (c) Draw vector diagrams to determine the direction of the total acceleration for these two positions. (d) Calculate the magnitude and direction of the total acceleration at these two positions.Explanation / Answer
1.
a)
Lisa :
Vi = 0 m/s
a1 = 3i - 2j
t = 5
velocity after 5 sec is given as ::
V1= a1 t
V1= (3i - 2j) 5
V1= 15 i - 10 j
Jill :
Vi = 0 m/s
a2 = 1i + 3j
t = 5
velocity after 5 sec is given as ::
V2 = a2 t
V2 = (1i + 3j) 5
V2= 5 i + 15 j
Lisa's speed relative to jill is given as
V1 - V2 = 15 i - 10 j - (5 i + 15 j) = 10 i - 25 j
b)
distance travelled by Lisa ::
d1 = Vi t + (0.5) a1 t2
d1 = (0)(5) + (0.5) (3i - 2 j) (5)2
d1 = 37.5 i - 25 j
distance travelled by Lisa ::
d2 = Vi t + (0.5) a2 t2
d2 = (0)(5) + (0.5) (1i + 3 j) (5)2
d2 = 12.5 i + 37.5 j
distance between Lisa and jill
d1 - d2 = (37.5 i - 25 j) - (12.5 i + 37.5 j) = 25 i - 62.5 j
c)
Lisa's acceleration realtive to Jill's ::
a1 - a2 = (3i - 2j) - (1i + 3j) = 2 i - 5 j
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