Question

A stunt cyclist needs to make a calculation for an upcoming cycle jump. The cyclist is traveling 100 ft/sec toward an inclined ramp which ends 10 feet above a level landing zone. Assume the cyclist maintains a constant speed up the ramp and the ramp is inclined Ao (degrees) above horizontal. With the pictured imposed coordinate system, the parametric equations of the cyclist will be: x(t) = 100t cos(A) y(t) = –16t2 + 100t sin(A) + 10. (These are the parametric equations for the motion of the stunt cyclist.)If the cyclist wants to have a maximum height of 35 feet above the landing zone, then the required launch angle is A=

Answer 1

Answer:$A=23.57^{\circ}$

Explanation:

Given

velocity=100 ft/s

height of landing zone=10 ft

Equation of $x(t)=100 t\cos (A)$

$y(t)=-16t^2+100t\sin (A)+10$

Maximum height=35 feet

at maximum height

$\frac{\mathrm{d} Y}{\mathrm{d} t}=0$

$\frac{\mathrm{d} x}{\mathrm{d} t}=-32t+100\sin A$

$t=3.125\sin A$

At $t=3.125\sin A$

$Y(t)=35=-16\times (3.125\sin A)^2+100\times 3.125\sin A\times \sin A+10$

$312.5\sin^2 A-156.25\sin^2 A=25$

$sin^2 A=0.16$

$A=23.57^{\circ}$