Problem 1 :
A missile fired ground level rises x meters vertically upwards in t seconds and x = 100t - (25/2)t^{2}. Find
(i) the initial velocity of the missile,
(ii) the time when the height of the missile is a maximum
(iii) the maximum height reached and
(iv) the velocity with which the missile strikes the ground.
Problem 2 :
A particle of unit mass moves so that displacement after t seconds is given by x = 3 cos (2t - 4). Find the acceleration and kinetic energy at the end of 2 seconds. K.E = (1/2) m v^{2 }Solution
Problem 3 :
The distance x meters traveled by a vehicle in time t seconds after the brakes are applied is given by
x = 20 t - (5/3)t^{2}
Determine
(i) the speed of the vehicle (in km/hr) at the instant the brakes are applied and
(ii) the distance the car traveled before it stops.
Problem 4 :
Newton's law of cooling is given by θ = θ₀° e^{⁻kt}, where the excess of temperature at zero time is θ₀° C and at time t seconds is θ° C. Determine the rate of change of temperature after 40 s given that θ₀ = 16° C and k = -0.03.(e^{1.2} = 3.3201) Solution
Problem 5 :
The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm²/min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100 cm^{2}. Solution
Problem 6 :
At noon, ship A is 100 km west of ship B. Ship A is sailing east at 35 km/hr and ship B us sailing north at 25 km/hr. How fast is the distance between the ship changing at 4.00 p.m Solution
Problem 7 :
Two sides of a triangle are 4 m and 5 m in length and the angle between them is increasing at the rate of 0.06 rad/sec. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is π/3. Solution
Problem 8 :
Two sides of a triangle have length 12 m and 15 m. The angle between them is increasing at a rate of 2°/min. How fast is the length of third side increasing when the angle between the sides of fixed length is 60° ? Solution
Problem 9 :
Gravel is being dumped from a conveyor belt at a rate of 30 ft³/min and its coarsened such that it forms a pile in the shape of cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high? Solution
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