If h (0) = 20meters, what is the maximum height? Give an exact answer with units

Question

If h(0) = 20meters, what is the maximum height? Give an exact answer with units.

2. The table below gives the height, h, of a falling object (in feet) at various times, t (in seconds).

When is the velocity of the object ?30ft/s? Round to the nearest quarter of a second.

h (ft) 70 69 66 61 54 46 37 27 17 t (s) 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 A projectile is launched straight up. Its height, h, is measured in meters. Time, t, is in seconds. The graph below shows the rate of change ofh in units of meters per second. If h(0) = 20meters, what is the maximum height? Give an exact answer with units. 2. The table below gives the height, h, of a falling object (in feet) at various times, t (in seconds). When is the velocity of the object ?30ft/s? Round to the nearest quarter of a second. h (ft) 70 69 66 61 54 46 37 27 17 t (s) 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Explanation / Answer

a) Slope of the line: -3

Equation of the line: h'(t) = 15 - 5t

h(t) = 15t - 2.5t2 + c. As h(0) = 20, c = 20. Therefore h(t) = 15t - 2.5t2 + 20.

h'(t) = 0 when 15 - 5t = 0 when t = 3. Hence h(t) is maximum when t = 3.

h(3) = 42.5 is the maximum height.

b) Observe that h(t) = 70 - (4t)2

h'(t) = -8t = -30 => t = 3.75

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