Question

1.  If a − b = 2c, a + b = 4c and c = 3i + 4j, then what is a and b? 
2. a. An electron moving along the x-axis has a position given by x = (16te−t ) m, where t is in seconds. How far is the electron from the origin when it momentarily stops? 
3.  A projectile is launched from ground level with speed u at an angle of  above the horizontal. Find in terms of u,  and g by proving: I. the maximum height H attained by the projectile, II. the distance from the starting point at which the projectile strikes the ground; this is called the range R of the projectile. III. The total time of flight 

Answer 1

1)

$$\bold{2a=6c}\\\bold{a=9i+12j}$$

$$\bold{2b=2c}\\\bold{a=3i+4j}$$

2)

$$v(t)=16e^{-t}-16te^{-t}=0\\t=0.0625\ s$$

$$x=16(0.0625)e^{-0.0625}=0.939\ m$$

3)

$$H=\frac{u^2\sin^2\theta}{2g}\\R=\frac{u^2\sin 2\theta}{g}\\T=\frac{2u\sin\theta}{g}$$