Respuesta :
Answer:13 ft/s
Explanation:
Given
Balloon velocity is 2 ft/s upwards
Distance between balloon and cyclist is 70 ft
Velocity of cyclist is 19 ft/s
After 3 sec
cyclist traveled a distance of [tex]d_c=19\times 3=57 ft[/tex]
Distance traveled by balloon in 3 s
[tex]d_b=2\times 3=6 ft[/tex]
net height of balloon from ground =6+70=76 ft[/tex]
at [tex]t=3 s[/tex]
distance between cyclist and balloon is [tex]z=\sqrt{76^2+57^2}[/tex]
[tex]z=95 ft[/tex]
now suppose at any time t cyclist cover a distance of x m and balloon is at a height of h m
thus [tex]z^2=x^2+y^2[/tex]
differentiating w.r.t time
[tex]2 z\cdot \frac{\mathrm{d} z}{\mathrm{d} t}=2 x\cdot \frac{\mathrm{d} x}{\mathrm{d} t}+2 y\cdot \frac{\mathrm{d} y}{\mathrm{d} t}[/tex]
[tex]z\cdot \frac{\mathrm{d} z}{\mathrm{d} t}=x\cdot \frac{\mathrm{d} x}{\mathrm{d} t}+ y\cdot \frac{\mathrm{d} y}{\mathrm{d} t}[/tex]
[tex]z\cdot \frac{\mathrm{d} z}{\mathrm{d} t}=57\times 19+76\times 2[/tex]
[tex]\frac{\mathrm{d} z}{\mathrm{d} t}=\frac{1235}{95}=13 ft/s[/tex]
