hi,
can someone help me? my exams are on Monday and I'm kinda lost with the whole application of calculus topic
so i need someone to go through these questions for me and HELP ME PLEASE!! Some of them are quite basic but I still get them wrong :mad1: .
1) A car is driven on a horizontal road at 20m/s when it goes a 30m cliff. Find the minimum speed it needs to travelat for the angle to be 45 or less when it hits the ground.
2) The displacement of a particle movingin a straight line is given by x=cost + sint. Find the maximum velocity.
3) A car amd a plance race each other down a runway. The car increases its speed v1 at a constant rate, while the speed of the plance is given by v2=2t^2. after 5 seconds, the car and the plane have the same speed. When does the plane overtake the car?
4) A tennis ball is served from a height of 1.8m in a horizontal direction at 35m/s. Find the distance the ball clears the 0.95m net which is 14m from the position it is served.
5) A particle moving in SHM has a period of motion 4sec. the particle starts moving towards the origin with a speed of pi-root3cm/sec form a point 2cm on the positive side of the rogin. Find when the particle is 2cm on the negative side of the origin for the second time.
6) A particle moving in SHM makes 10 complete oscillations per minute. If its maximum speed is pi cm/s, find the amplitude of the motion.
7) A particle at rest is acted on by acceleration given by a=6t-6. How long will it take to return to its initial position?
8) A particle starts from rest, 3 cm to the right of the roigin, with initial acceleration -12cm/s/s. Find the displacement as a function of time.
9) A particle moves wiht velocity v m/s where v^2=4x+1 and the particle starts at the origin. Find velocity when displacement is 6m. How do I know whether it's positive or negative?
10) If x=3sin(t+pi/3), what would the equation be if cos was used instead of sin?
11) water sprays from a leak in a hose. if it reaches a height of 2m and travels a distance of 8 m, find how long each droplet of water is in the air.
12) A stone is thrown so it will hit a bird at the top of a pole. At the instant the stone is thrown the bird flies off in a horizontal direction in a straight line directly away from the point of projection at a speed of 10m/s. The stone reaches a height of twice that of the pole and on the way down it hits the bird. Find the horizontal velocity of the stone. There is a similar question in Terry Lee's book but it doesn't make sense.
13) A particle is projected to just clear 2 walls of height 7 m and distant 7m and 14m form the projection point. Show that the angel of projection is arctan(3/2)
14) A particle is projected witha speed of 25m/s in the direction of a point P which is 24m horizontally and 7m vertically above the point of porjection. Find the distance directly below P when the particle passes.
thanks kind stranger (s).
can someone help me? my exams are on Monday and I'm kinda lost with the whole application of calculus topic
so i need someone to go through these questions for me and HELP ME PLEASE!! Some of them are quite basic but I still get them wrong :mad1: .1) A car is driven on a horizontal road at 20m/s when it goes a 30m cliff. Find the minimum speed it needs to travelat for the angle to be 45 or less when it hits the ground.
2) The displacement of a particle movingin a straight line is given by x=cost + sint. Find the maximum velocity.
3) A car amd a plance race each other down a runway. The car increases its speed v1 at a constant rate, while the speed of the plance is given by v2=2t^2. after 5 seconds, the car and the plane have the same speed. When does the plane overtake the car?
4) A tennis ball is served from a height of 1.8m in a horizontal direction at 35m/s. Find the distance the ball clears the 0.95m net which is 14m from the position it is served.
5) A particle moving in SHM has a period of motion 4sec. the particle starts moving towards the origin with a speed of pi-root3cm/sec form a point 2cm on the positive side of the rogin. Find when the particle is 2cm on the negative side of the origin for the second time.
6) A particle moving in SHM makes 10 complete oscillations per minute. If its maximum speed is pi cm/s, find the amplitude of the motion.
7) A particle at rest is acted on by acceleration given by a=6t-6. How long will it take to return to its initial position?
8) A particle starts from rest, 3 cm to the right of the roigin, with initial acceleration -12cm/s/s. Find the displacement as a function of time.
9) A particle moves wiht velocity v m/s where v^2=4x+1 and the particle starts at the origin. Find velocity when displacement is 6m. How do I know whether it's positive or negative?
10) If x=3sin(t+pi/3), what would the equation be if cos was used instead of sin?
11) water sprays from a leak in a hose. if it reaches a height of 2m and travels a distance of 8 m, find how long each droplet of water is in the air.
12) A stone is thrown so it will hit a bird at the top of a pole. At the instant the stone is thrown the bird flies off in a horizontal direction in a straight line directly away from the point of projection at a speed of 10m/s. The stone reaches a height of twice that of the pole and on the way down it hits the bird. Find the horizontal velocity of the stone. There is a similar question in Terry Lee's book but it doesn't make sense.
13) A particle is projected to just clear 2 walls of height 7 m and distant 7m and 14m form the projection point. Show that the angel of projection is arctan(3/2)
14) A particle is projected witha speed of 25m/s in the direction of a point P which is 24m horizontally and 7m vertically above the point of porjection. Find the distance directly below P when the particle passes.
thanks kind stranger (s).
