Applications of trigonometric functions
Interactive practice questions
When a vehicle travels uphill or downhill, it experiences a force due to gravity. This force, $F$F, in Newtons is the called the grade resistance and is modelled by the formula $F=W\sin\theta$F=Wsinθ, where $W$W is the weight of the car in Newtons and $\theta$θ is the angle of inclination.
Find the grade resistance of a car with a weight of $10700$10700 Newtons travelling uphill at a slope of $5.1^\circ$5.1°. Give your answer to the nearest Newton.
When a vehicle travels uphill or downhill, it experiences a force due to gravity. This force, $F$F, in Newtons ($N$N) is the called the grade resistance and is modelled by the formula $F=W\sin\theta$F=Wsinθ, where $W$W is the weight of the car in Newtons and $\theta$θ is the angle of inclination in degrees.
From a parking lot, you want to walk to a house on the beach. The diagram shows that the house is located $1200$1200 feet down a paved path that parallels the ocean, which is $500$500 feet away.
Along the path you can walk $300$300 feet per minute, but in the sand on the beach you can only walk $100$100 feet per minute.
The time $T$T minutes to get from the parking lot to the beach house expressed as a function of the angle $\theta$θ shown is $T\left(\theta\right)=4-\frac{5}{3\tan\theta}+\frac{5}{\sin\theta}$T(θ)=4−53tanθ+5sinθ
The formula $d=\frac{1}{32}v^2\sin2\theta$d=132v2sin2θ gives the distance $d$d (in feet) that a projectile will travel when its launch angle is $\theta$θ (in degrees) and its initial velocity is $v$v (in feet per second) where $v>0$v>0.