Question

The Dik-dik is the smallest antelope. They are 30 cm tall. One jumps over a creek. The creek is 10m wide.

(a) If the Dik-dik we are watching jumps, from the edge of the creek, with speed 10.0m/s at an angle of 30 degrees above the horizontal. Set the origin to be the original location of the Dik-dik, and upwards and to the right are both increasing (as shown). What are the components of the initial velocity vector

(b) What will the components of the instantaneous velocity vector be when the Dik-dik is at the maximum height?

(c) What are the components of the acceleration vector when the Dik-dik is at the maximum height?

(d) How much time does it take for the Dik-dik to go from its initial position, to the location of its maximum height

(e) How much time does the Dik-dik spend in the air before it lands?

(f) Does the Dik-dik successfully jump over the creek?

(g) If the Dik-Dik jumped at an angle 45 degrees above the horizonal, would they make it over the creek?

Answer 1

(a)

$v_{ix}=10\cos 30^{\circ}=8.66\: m/s$

$v_{iy}=10\sin 30^{\circ}=5\: m/s$

(b)

$v_{fy}=0$

(c)

$a_{fx}=0$

(d)

$t=\frac {v_{iy}}{g}=\frac {5}{9.8}\: s = 0.51\: s$

(e)

$T=\frac {2v_{iy}}{g}=\frac {2\cdot 5}{9.8}\: s =1.02\: s$

(f)

$D=v_{ix}T= (8.66\times 1.02)m=8.83\: m$

No, it doesn't jump successfully.

(g)

$D=v_{ix}T= (10\cos 45^{\circ}\times 1.02)m=7.21\: m$

No, they won't make it over the creek.