7/17/2019 PC1431 Tutorial 1

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Tutorial 1

Question 1

A boy stands at the peak of a hill which slopes downwards uniformly at an angle  φ asshown in Figure 1. At what angle  θ  from the horizontal should he throw a rock so thatit has the greatest range,  R?

v

φ

θ

φ

R

Figure 1: Calculating the angle for maximum distance

[Ans:   θ =  π/4 − φ/2]

Question 2

A particle leaves the origin at  t  = 0 with an initial velocity  v0  = 3.6 i  ms−

1 along thex-axis. It experiences an acceleration a = −1.2t

˜i− 1.4

˜ j   ms−2. At what time  T   does

the particle reach its maximum  x value?[Ans:   t =

√ 6 ≃ 2.45 s ]

Question 3

A car moving at 18.1 ms−1 enters a curve that describes a quarter turn of radius 120m from  A to  B  as shown in Figure 2.

1

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B

R

A

Figure 2: Turning a corner

The driver gently applies the brakes, slowing the car down at a constant rate of 0.65 ms−2. Just before emerging from the turn at  B, what is the angle between the

acceleration vector and the direction of motion?[Ans: 133◦]

Question 4

A small boat is headed for a harbour 32 km north-west of its current position whenit is suddenly engulfed in a heavy fog. The captain maintains a compass bearing of north-west and a speed of 10 km/hr relative to the water. Three hours later the foglifts and the captain notes that he is now exactly 4.0 km south of the harbour. Takingı   to be directed along east and ˆ    to be directed north, what is the velocity  v   of the

current during those three hours? (You may assume that  v  is a constant.)[Ans:  v = −(0.47km/hr) ı− (0.86km/hr)ˆ ]

Question 5: For Practice

A particle has a position vector given by

r(t) = 3.0t2˜i +

4.0t3 − 5.0t4

˜ j   (1)

where  r   is in meters and   t   is in seconds. Find the average velocity and average accel-

eration from  t = 2.0 s to  t = 4.0 s.[Ans:  vavg = 18 ı− 488ˆ   m/s,   aavg = 6.0 ı− 488 ˆ   m/s2]

Question 6: For Practice

An Engineering Physics student buys a plastic dart gun. Being a clever student shedecides to do a quick calculation to find its maximum horizontal range. To find out,she shoots the gun  straight up, and it takes 5.0 seconds for the dart to land back in thebarrel. What is the maximum horizontal range of the gun? Ignore air resistance.[Ans: 61.3 m]

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