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**Extra info for Applied Mathematics by Example: Exercises**

**Example text**

D) Find out the time at which this distance is smallest and verify that the distance of closest approach of the two ships is 8 km. Hint: if the distance AB is d, the mathematics may work out most easily if you consider how d2 varies with time. 19. Particle P has velocity 10i + kj m/s. If the speed of P is 26 m/s, what is k? 20. Particle Q has velocity 5i + k(i + 2j) m/s. What value of k is needed to make the velocity of Q (a) parallel to the vector i + j, (b) parallel to the vector i and (c) parallel to the vector j.

Repeat the calculation for (a) a slope with a straight line profile SF and (b) any other profile of your own choosing, and verify that the final speed at F remains the same in each case. com 42 Click on the ad to read more Questions Applied Mathematics by Example: Exercises 8. A particle of mass m is projected with speed V up a rough slope which is inclined at an angle θ to the horizontal. The coefficient of friction between the particle and the slope is µ. Show that the maximum distance x travelled up the slope by the particle before it starts to slide down again is given by the formula x = V2 .

3 m. 10. A spherical egg of diameter 5 cm and mass 60 g is dropped from a height of 2 m onto a concrete floor. (a) Calculate the speed at impact. (b) What is the change in momentum of the egg? (c) Show that the time difference between the instant when the bottom of the egg first touches the floor and the instant when the top of the egg follows it down to floor level is about 8 milliseconds. (d) Estimate the average force applied to the egg while the impact lasts. 11. * Ten identical railway trucks are lined up on a railway track with 10 m spacing between consecutive trucks.