Two stones are thrown with the same initial speed at the same instant from the roof of a building. One stone is thrown at an angle of 30 degree above the horizontal; the other is thrown horizontally.(Neglect air resistance.), which of the following is true:_________
(a)The stones strike the ground at the same time and with equal speeds.
(b)The stones strike the ground at the same time with different speeds.
(c)The stones strike the ground at different times with equal speeds.
(d)The stones strike the ground at different times with different speeds.

Option a is not true because of the angle the first stone is thown at. Due to this angle, the stone will travel for some time upwards, which will give an advantage to the first stone which was thrown horizontally, being this one the first to reach the ground.

Option b is not true, since as stated on the first paragraph, the horizontally thrown stone will fall first, due to the advantage given by the angle of the first stone.

Option d is not true because even though they do not strike the ground at the same time, their speed must be the same. (Notice there is a difference between speed and velocity. Velocity is a vector which has magnitude and direction while speed is just a scalar which will have onlly magnitude.)

Due to energy conservation, if we don't take the resistance of air into account, then the speeds of both stones must be the same since energy is conserved. They will have the same amount of potential and kinetic energy in the beginning, so the potential and kinetic energy must be the same in the end, this is when they hit the ground. The potential energy will become kinetic energy which will be the same for both stones. Their speeds will be the same even though their directions will be different.

So the answer is c) The stones strike the ground at different times with equal speeds.