Advertisements
Advertisements
प्रश्न
A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance of s = 16t2 in t seconds. What is the instantaneous velocity of the camera when it hits the ground?
Advertisements
उत्तर
f(t) = 16t2
f'(t) = 32t
f'(t) at t = 5 = 32(5)
= 160 ft/sec
APPEARS IN
संबंधित प्रश्न
A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance of s = 16t2 in t seconds. What is the average velocity with which the camera falls during the last 2 seconds?
A particle moves along a line according to the law s(t) = 2t3 – 9t2 + 12t – 4, where t ≥ 0. At what times the particle changes direction?
A particle moves along a line according to the law s(t) = 2t3 – 9t2 + 12t – 4, where t ≥ 0. Find the total distance travelled by the particle in the first 4 seconds
If the mass m(x) (in kilograms) of a thin rod of length x (in metres) is given by, m(x) = `sqrt(3x)` then what is the rate of change of mass with respect to the length when it is x = 3 and x = 27 metres
A beacon makes one revolution every 10 seconds. It is located on a ship which is anchored 5 km from a straight shoreline. How fast is the beam moving along the shoreline when it makes an angle of 45° with the shore?
A police jeep, approaching an orthogonal intersection from the northern direction, is chasing a speeding car that has turned and moving straight east. When the jeep is 0.6 km north of the intersection and the car is 0.8 km to the east. The police determine with a radar that the distance between them and the car is increasing at 20 km/hr. If the jeep is moving at 60 km/hr at the instant of measurement, what is the speed of the car?
Find the slope of the tangent to the following curves at the respective given points.
y = x4 + 2x2 – x at x = 1
Find the point on the curve y = x2 – 5x + 4 at which the tangent is parallel to the line 3x + y = 7
Find the tangent and normal to the following curves at the given points on the curve
y = x2 – x4 at (1, 0)
Find the tangent and normal to the following curves at the given points on the curve
y = x sin x at `(pi/2, pi/2)`
Find the tangent and normal to the following curves at the given points on the curve
x = cos t, y = 2 sin2t at t = `pi/2`
Find the equations of the tangents to the curve y = 1 + x3 for which the tangent is orthogonal with the line x + 12y = 12
Find the equations of the tangents to the curve y = `- (x + 1)/(x - 1)` which are parallel to the line x + 2y = 6
Find the equation of tangent and normal to the curve given by x – 7 cos t andy = 2 sin t, t ∈ R at any point on the curve
Find the angle between the rectangular hyperbola xy = 2 and the parabola x2 + 4y = 0
Show that the two curves x2 – y2 = r2 and xy = c2 where c, r are constants, cut orthogonally
Choose the correct alternative:
The position of a particle moving along a horizontal line of any time t is given by s(t) = 3t2 – 2t – 8. The time at which the particle is at rest is
Choose the correct alternative:
A stone is thrown, up vertically. The height reaches at time t seconds is given by x = 80t – 16t2. The stone reaches the maximum! height in time t seconds is given by
Choose the correct alternative:
The slope of the line normal to the curve f(x) = 2 cos 4x at x = `pi/12` is
Choose the correct alternative:
Angle between y2 = x and x2 = y at the origin is
