Range is the horizontal distance covered during the total time of flight.
0=(usinθ)T−12gT2space 0 equals open paren u sine theta close paren cap T minus one-half g cap T squared
L⃗=r⃗×p⃗space modified cap L with right arrow above equals modified r with right arrow above cross modified p with right arrow above Differentiating with respect to time ( ) using the product rule:
When a vehicle takes a sharp turn on a flat road, friction alone provides the necessary centripetal force. To prevent skidding and minimize tire wear, roads are tilted inward at an angle be the mass of the vehicle, be the normal reaction force, and be the coefficient of static friction.
mv2R=Nsinθ+fcosθthe fraction with numerator m v squared and denominator cap R end-fraction equals cap N sine theta plus f cosine theta
ghg=R2(R+h)2=(1+hR)-2the fraction with numerator g sub h and denominator g end-fraction equals the fraction with numerator cap R squared and denominator open paren cap R plus h close paren squared end-fraction equals open paren 1 plus the fraction with numerator h and denominator cap R end-fraction close paren to the negative 2 power Using Binomial approximation for
Range is the horizontal distance covered during the total time of flight.
0=(usinθ)T−12gT2space 0 equals open paren u sine theta close paren cap T minus one-half g cap T squared
L⃗=r⃗×p⃗space modified cap L with right arrow above equals modified r with right arrow above cross modified p with right arrow above Differentiating with respect to time ( ) using the product rule:
When a vehicle takes a sharp turn on a flat road, friction alone provides the necessary centripetal force. To prevent skidding and minimize tire wear, roads are tilted inward at an angle be the mass of the vehicle, be the normal reaction force, and be the coefficient of static friction.
mv2R=Nsinθ+fcosθthe fraction with numerator m v squared and denominator cap R end-fraction equals cap N sine theta plus f cosine theta
ghg=R2(R+h)2=(1+hR)-2the fraction with numerator g sub h and denominator g end-fraction equals the fraction with numerator cap R squared and denominator open paren cap R plus h close paren squared end-fraction equals open paren 1 plus the fraction with numerator h and denominator cap R end-fraction close paren to the negative 2 power Using Binomial approximation for