A stone is dropped from a balloon moving upwards with velocity 20m/s when the balloon is at height 60m

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We have a physics problem involving projectile motion. A stone is dropped from a balloon that is moving upward at twenty meters per second. The balloon is at a height of sixty meters when the stone is released. The stone inherits the balloon's upward velocity and is then acted upon by gravity. To analyze this motion, we use kinematic equations. The position equation is h equals h naught plus v naught t plus one half a t squared. The velocity equation is v equals v naught plus a t. Substituting our values, we get h of t equals sixty plus twenty t minus four point nine t squared, and v of t equals twenty minus nine point eight t. The stone initially moves upward, but gravity slows it down until it reaches maximum height when velocity becomes zero. To find the maximum height, we first determine when the velocity becomes zero. Setting v of t equals twenty minus nine point eight t equal to zero, we solve for t equals twenty divided by nine point eight, which is two point zero four seconds. Then we substitute this time into the position equation to get h maximum equals eighty point four meters. This is the highest point the stone reaches before falling back down. To find when the stone hits the ground, we set the height equation equal to zero. This gives us sixty plus twenty t minus four point nine t squared equals zero. Rearranging to standard form and using the quadratic formula, we get t equals twenty plus or minus thirty nine point seven, all divided by nine point eight. Taking the positive solution, the stone hits the ground at t equals six point zero nine seconds. To summarize our analysis: A stone dropped from a balloon moving upward at twenty meters per second from sixty meters height reaches a maximum height of eighty point four meters after two point zero four seconds. The stone then falls and hits the ground after a total flight time of six point zero nine seconds. This demonstrates classic projectile motion where initial upward velocity temporarily overcomes gravity before the stone follows a parabolic path back to earth.