Answer to Question #109635 in Mechanics | Relativity for Ankur kumar

Question

rabbit run across a parking lot on which set of coordinates axes has been drawn. The coordinates (in metres) of the rabbits position as function of time (in second) are given by:-
x= -0.32t² + 7.2t + 28
y= 0.22t² - 9.1t + 30
At t=15 s, what is the rabbits position for r in unit vector notation and in magnitude angle notation?
i. Draw a graph for rabbits path for t= 0 to t= 25 s
ii. Find the rabbits velocity v at time t= 15 s
iii. Find the rabbits acceleration 'a' at time t= 15 s.

Answer 1

Given:

$x(t)=-0.32t^2+7.2t+28$

$y(t)=0.22t^2-9.1t+30$

The rabbit position at $t=15\:\rm s$

$${\bf r}=64{\hat i}-57{\hat j}=(86; 318\degree)$$

(i) rabbit path

(ii) rabbit velocity

$${\bf v}=-2.4{\hat i}-2.57{\hat j} \:(\rm m/s)$$

(iii) rabbit acceleration

$${\bf a}=-0.64{\hat i}+0.44{\hat j} \:(\rm m/s^2)$$