A particle P projected from a point O on horizontal ground hits the ground after 2.4 seconds. The horizontal component of the initial velocity of P is 5/3 d ms-1 (a) Find, in terms of d, the horizontal distance of P from O when it hits the ground. (b) Find the vertical component of the initial velocity of P. P just clears a vertical wall which is situated at a horizontal distance d meter from O. (c) Find the height of the wall.

At time t20, the acceleration of a particle moving on the x-axis is a(t) =t+sint. At t= 0, the velocity of the particle is -2. For what value t will the velocity of the particle be zero? (A) 1.02 (B) 1.48 (C) 1.85 (D) 2.81 (E) 3.14

) An object is thrown upward at time t = 0. After t seconds, its height is y = −4.9t² + 2t + 4.5 meters above the ground. (a) From what height was the object thrown? (b) What is the initial velocity of the object? (c) What is the acceleration due to gravity? meters m/s m/s²

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The area of a circle increases at a rate of 2 cm² /s. How fast is the radius changing when the radius is 5cm? a) Draw the picture. b) Write the given and unknown derivatives in d/dt notation. c) Label the variables. d) Proceed to solve and finish the problem. Reminder, keep solutions and answer in exact form and don't forget the units on the final answer.

Elena was pouring coffee at a constant rate into a mug similar to the one shown in the figure. Counting the seconds to fill the mug with coffee, Elena calculated that she is pouring coffee at 25ml/sec. The mug has a height of 10 cm and it took Elena about 5 seconds to fill the mug to the brim. Sketch a graph of the depth of the coffee in the mug as a function of time. Account for the shape of the graph in terms of concavity. By looking at your graph, describe how the depth of the coffee in the mug is changing and answer the following: a) At first, the depth of the coffee in the mug is changing at a (Key words for your description: rate, faster, slower). I know that, because Then, the depth of the coffee is increasing at a b) Around second the mug is filling at the fastest rate. I estimate that, at that time, the depth of the coffee would be about cm. C) The inflection point of the function would be The inflection point is the point where d) The average rate of change of the depth of…

b. A particle moves in simple harmonic motion according to the equation, S = 09A cos(wt) + 09B cos(wt). Where s is the displacement, w is the angular d2 +ws=0. 'dt2 frequency and A, B are constant. Show that,

A particle P projected from a point O on horizontal ground hits the ground after 2.4 seconds. The horizontal component of the initial velocity Of P is ms¯l. (a) Find, in termsofd, the horizontal distance ofPfrom O when it hits the ground. (b) Find the vertical commM1ent of the initial velocity of P. P just clears a vertical wall which is situated at a horizontal distance dm from O. (c) Find the height of the wall. The speed of pas it passes over the wall is 16m (d) Find the value Of d correct to 3 significant figures, o_2kg